Remarks about the self  similar solutions of the Vortex Filament Equation
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Title 
Remarks about the self  similar solutions of the Vortex Filament Equation

Title of Series  
Part Number 
11

Number of Parts 
21

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License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2016

Language 
English

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Subject Area  
Abstract 
I will review some of the properties of the selfsimilar solutions of the Vortex Filament Equation. This equation is also known as either the Localized Induction Equation or the binormal flow and is related to the 1d Schrodinger map and the 1d cubic nonlinear Schrodinger equation. After looking at the uniqueness and asymptotic behavior of these solutions, I will recall the method developed with V. Banica to continue the solution once the singularity (a corner) is created. Issues concerning the lack of the preservation of linear momentum and the nocontinuity of some critical Besov norms will be considered. Finally I will mention some recent work done with F. De La Hoz about the evolution of a regular polygon

00:00
Point (geometry)
Ocean current
Computer programming
Group action
Observational study
INTEGRAL
Logarithm
Multiplication sign
Image resolution
Decision theory
1 (number)
Mereology
Event horizon
Product (business)
Vortex
Frequency
Derivation (linguistics)
Lecture/Conference
Velocity
Different (Kate Ryan album)
Square number
Energy level
Körper <Algebra>
Nichtlineares Gleichungssystem
Rotation
Dependent and independent variables
Theory of relativity
Mass flow rate
Physical law
Model theory
Moment (mathematics)
Evolute
Sphere
Approximation
Connected space
Curvature
Voting
Right angle
Musical ensemble
Maß <Mathematik>
09:46
Polar coordinate system
Group action
Dynamical system
INTEGRAL
State of matter
Multiplication sign
Direction (geometry)
Special unitary group
Grothendieck topology
Variance
Plane (geometry)
Square number
Circle
Extension (kinesiology)
Position operator
Social class
Physical system
Rhombus
Area
Concentric
Closed set
Lattice (order)
Hand fan
Curvature
Arithmetic mean
Ring (mathematics)
Vector space
Phase transition
Dew point
Normal (geometry)
Right angle
Cycle (graph theory)
Relief
Spacetime
Point (geometry)
Computer programming
Functional (mathematics)
Momentum
Observational study
Transformation (genetics)
Parity (mathematics)
Image resolution
Maxima and minima
3 (number)
Similarity (geometry)
Translation (relic)
Mass
Vortex
Lecture/Conference
Complex number
Theorem
Nichtlineares Gleichungssystem
Analytic continuation
Summierbarkeit
Set theory
Condition number
Addition
Sine
Military base
Forcing (mathematics)
Projective plane
Model theory
Content (media)
Mathematical analysis
Algebraic structure
Total S.A.
Basis <Mathematik>
Line (geometry)
Latent class model
Cartesian coordinate system
Evolute
Numerical analysis
Game theory
Musical ensemble
Maß <Mathematik>
29:19
Logical constant
Group action
State of matter
Multiplication sign
Direction (geometry)
Orientation (vector space)
Correspondence (mathematics)
Range (statistics)
1 (number)
Proper map
Food energy
6 (number)
Explosion
Derivation (linguistics)
Mathematics
MKS system of units
Different (Kate Ryan album)
Forest
Square number
Series (mathematics)
Rotation
Process (computing)
Block (periodic table)
Generating set of a group
Curve
Infinity
Maxima and minima
Special unitary group
Lattice (order)
Curvature
Arithmetic mean
Angle
Symmetry (physics)
Chain
Order (biology)
Normal (geometry)
Right angle
Thermal conductivity
Spacetime
Point (geometry)
Ocean current
Existence
Line (geometry)
Real number
Letterpress printing
Similarity (geometry)
Student's ttest
Average
Event horizon
Goodness of fit
Causality
Lecture/Conference
Term (mathematics)
Energy level
Nichtlineares Gleichungssystem
Analytic continuation
Set theory
Condition number
Standard deviation
Uniqueness quantification
Line (geometry)
Latent class model
Binary file
Numerical analysis
Diameter
Game theory
46:49
Classical physics
Group action
Dynamical system
Length
State of matter
Connectivity (graph theory)
Multiplication sign
Maxima and minima
Student's ttest
Population density
Symmetry (physics)
Lecture/Conference
Triangle
Conservation law
Modulform
Right angle
Physical system
Condition number
Distortion (mathematics)
51:55
Point (geometry)
Lecture/Conference
Multiplication sign
Projective plane
Charge carrier
Right angle
Nichtlineares Gleichungssystem
Curve fitting
Spectrum (functional analysis)
Product (business)
Wave packet
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09:48
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19:34
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positive look at this these equation of soil has more than 1 possible escaping but if you really want to preserve their their fog you want this is the only possible 1 and of course is the 1 that also comes when you once you start saying that talks and bus in this proceeding city so now I want to find a solution of that's the minimum of real problem under the city's so you will agree to this country and all and they duly censored again you will obtain calling covered that the the corresponding derivatives then immediately you obtain minus pursuant to promptly close then the growth but his 2nd prime and then you used in this case and frame and you immediately see but then the corruption that has to a constant and that also has to make this sort of because of this is that he same to be menu have a nice reality could In an Infiniti and of course to the starting with the necessary you respect and then we will deal will with blasts all of these guys are used to this I'm this is a question 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something of a long always look at it and is that fact that was it confuse all the angles but so so this is in my 1st meeting flat and it would reduce the younger would have to consider the events even of very close formalizing the scientist in the world do not speak to mind strike this year's work over to side of our business uniqueness this 6th in existence for all I'm going on angles of except when the to rectify 1 the opposite of the other 1 and also gives you uniqueness In fact then you can quickly did more under which takes in a lot of money and you can say that the office is precisely a plusminus the 1st 2007 although various things that normal last fall of 1 arrests for sales and give them 1 and and that they buy nor among if the air is a square the floor plus some got extended this of course is completely innocent that the the huge dealing with something of his captain and is heading problem because they give you information at sea and I may ask something else was representing the meeting shoulders not correction he said because we all know that they're discovering provision regions long range sold for some was minus 0 1 over this with Disney blessed minus the standards to live it was miners and businesses some the Auerbach less kindly above and there also out of unity and let's look at victory moralists follows his these days to Morris see what hallways the picture of public energy because you know that grows to seal the destinies it also has to be close to say for sure and then at infinity history 2 mines in between to hover James Yukon kind of recent frozen there's there's something would be an exclusive beach that there will be a change in Rodessa essentially this year for the quotas will be the last 1 the and then of course without any information during the entire Corretja and this is information that in the hearts of all this is it's so this is wellknown now all their needs try to understand now use the questions about this guy and the first one yesterday that this was because of this from someone who is from the stories 1 legislative this broadening all to to to be able to complete a cross from 1 of these kind of problems existing than usual year the 2 2 have plenty plenty of symmetry to have such things Of course the season this is not a case of similar solutions you can have more of assessing the solutions for example the 1 that comes from the game's about money when arrests that building because by and those what I cannot beautiful like this there is no reason these ones that any I just show many worst enemy sold concerning then the 1st question this is if there were several worsening with the Moneyline income but at the end of the day we were able to pull out of this of the floor leaders In order to assess to the phone 2 glasses the 1st question I have to do really did you have to take to 2 but extends this solution and for a senior at that right now and I will do it as you would have run into him his talks related to this "quotation mark In this block to corresponding that goes for me at the time so you have always these synergy the plan for these out wouldn't occur so if a change the orientation meetings time showing the 2 chains orientation the only thing I have to go is to change his name to the diameter rests on the proper size for good cause that I can say saying this manufacturers way the following nite which is my status of film which is set it were effectively it's over the course of the 6 deposited and then as "quotation mark of cultural but did some rotation of GE professor letters critical
38:05
function but of the 4 kidnapping and the only thing need is to change the orientation should be their rotation that that they think customers will boost this time because of the the colony's cement and rotations of the number of the solution for the positivism was at the front of the harvesting season conditions of people wonder if this is a solution ,comma can sold interfering with Valaria it that yeah that takes the lead in a stable transition and the appropriate sentence and then and then use that effect makers moderation save you a remain close to the to the curve on budget that requirement is the same as he is smaller than the preparations of on other liberal the courage and the Dutch there is more in summer space that is related to less than of said that means that fell and that means that they can you want to be a generation of performance is sustainable and this is very important for the case of Little Rock because former Serbian disappeared faced with farright sold to 2 words some of this and was this is as I said the other repeal University and the 1st thing is that if I do it at the level of an unless many Norway and this is because if I make the case that so In the sees what is there to persevere under this situation the corresponding side of course is the 1 respect the story made at a time 1 I use that with my duration of student then we really want to construct a solution on the way tool the serial blasts but when you go schools still plans will die of stain so you 1 doesn't topics is likely see stories finally scored 215 today the square forests in this square poverty blasts then you have the problem of the long range of if the blast was the general say doesn't matter where you go this problem of the assessing and this is quite unique coming for all 4 of the almost all of them that's another fellas monotheists I can make a better reason across Ferguson was unable to defend him he here but this 1 does not have an image because of this of course this from the point of view has no the implications of the always have the feel of show you really want to know if this is having a problem not hide themselves that this series they knew that they had this kind of thing you need to know what that has to be precise the shares this kind of a unique way of continuing the problem when you go on to their genetics except current and the 2nd thing was that the inevitable this this information so would you are able to both is that your solution most signed by the end process and have delineates Europe over the important information which had a blast minutely the past mines that comes from the from the assisting solution and this is the 1 that W2 cost act the frame of time signal I want to continue and because you have it characterization of assessing solution then you can do so and what wanted to remember any of this fits pretty well for example when you see in a meeting with a kind of pictures among the penal of showing respect for the people living there must using images way so this assault on the 1st list and the 2nd question was blocked from this that in fact it's very easy to see that the union boss is not respect for the enables his desk in the setting is nothing but this produces call "quotation mark of the view Minnesota scope of could also be a facility would be in included so this is not the and years across the debts remember that's the satisfies that equation show of unity may have to is the and then the prime is so the only thing that remains is the normal so this is nothing but a minimum of prescribed dependent so consisting good which at times the normal which is the area of 4 of them all the abandoned and then what you're saying is that dependent that was minus infinity cousins values so this is precisely the paper last 1944 as it is unfortunate that if we Houston but we have to show that the meaning so this is for real so many angles is not a surprise of course because this energy or whatever is going to last line of conduct fair a cancer the 1st question in terms of the sun has more surprise of this for me which is as follows the fighting computer the norm both years which is the same as the courage of and this is 4 times 1 menus including minors by scene of the square this is for the people sitting on for different from versatile is 4 times by some I need insult that this number is secret Burundi's 1 specialists see note is not to focus so there is a lack of continuity In this photograph which said have had to make a picture of what's going on is a secular saint beaches you may just have to jump until this the because you are a little this because you have these nice for and then this is not so straightforward because for example if I go to the existing topics I have to pay attention to the next because completing the difference so this was some minimum of facts so now it's a very natural question can and what can I say when I spent with a reporter Frank and these are the pictures shown thank you so what we're going to do this where is the union movement and remember here news so what I'm going to show you it's what can I say for
46:51
example with any In the case of the of only 1 where you have many more symmetry found them well if you start to think a little bit about what they have just written a book at the front of this then you don't see this problem and in the case of course no Turkish
47:16
console the elemental has
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3 components these will be the 1st 1 9 the mining
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the 2nd 1 installed as a component will this 1 and you see that essentially concert in the theater with an ambush on the left of the right and then you go the other told by singing in the fairway into the of lights there's racing into the promise or what he said 10 you want to see that he said list when you look at the density of them for the Conservation Law a day sometimes from 1 place to another 1 and then you do all the things that I think everything in a closedcircuit viewing taking half of the and a so you have been the 1st and the 2nd component to this and would you see which is the classical picture of say for example that every man on the Financial Times and the city's intermittency aware of consumption fatalities this is 1 of the components and the other 1 is is 1 thing so this is what you and now this said city in the other question is what can I say to the maximum of their footing with use of the attended france I mean it this is the same it in this case and we made far he they was this fall and I'm going to compute this impact this time time to take the maximum and effective but the very visible symmetry when 1 is not till the other 1 the year the forms of anyway and this is the picture show this is for did you want the state to make it to so this is the maximum all this you're seeing I have respected the students because these these times higher I'm sorry I'm not rescinded the seventime time this time and it is a matter of course this speaks of the ocean there's monitoring nominated to be there Of course was going but that would definition Washington negotiators that was then and of course you don't is that you know you you you have transferred the from and offered to prove the Centers for them I think this is going to give and then yeah you could wander outside what happens here and if you do it probably Denny thinks that people will have to plenty of more experiments received very stringent and that we know how many so was a conclusion I don't think that they're in the right funds in estates the dynamics of the 2nd Reading system is much richer than what they would have expected combatants thank you to his this is in effect at the time of the Belgian politicians across Europe are so that the issue will increase the length of the services the cellular Over if you remain there as long as you have favored the conditions as to cause it peaks that Dixon will become as well as 1 there is a question of medicine here started with the distortion here but to delete them in there USA would and then made it so this is kind of dedicated because you really have to capture in demeanor makes a happens Arsenal times and then you wonder how are you willing to leave attention in a computer with here and there are some things that them and then well we had for quite some time the out of the system with the relevant have been given many listened but we
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weren't using their training there and the erotic products the thinking on a highticket point of view this traffic projection is that the right because then you have 1990 the but it does not that for the makes assisting the workers the death of the In fact we use the carrier may strongly that you don't and you have not does this equation but also the other finding makes you use 1st of all you can spectrum effort fell from that interview that makes what you're saying it sees fit that is stable the mother of all the furious on works pretty well meaning I don't understand why it works so well that you really want to have scientific and you want to arrest times and you see your 41 of intuition is I would say something because of course and then recovered scheme is necessary spectacles which is a reasonable thing to hear it but with the Newfoundland few him as