Almost global solutions for the capillarity wave equation...
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Almost global solutions for the capillarity wave equation...

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8

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21

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CC Attribution 3.0 Unported:
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2016

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English

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Abstract 
Almost global solutions for the capillarity wave equation with small periodic data We prove that the capillarity waves equation in one dimension and finite depth has solutions over time intervals of length c N\epsion^ for any N, if the Cauchy data are of small size \epsilon and space periodic, and if the gravity, or the surface tension, is taken outside a subset of zero measure. The proof relies on normal forms and on the use of the reversibility of the equation. This is joint work with Massimiliano Berti

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04:05
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22:23
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00:02
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you consider small In the danger so in that case you may explode to the specific properties of the question so that a solution souls in resignation we indicate when time goes to infinity in his allusion to prove that even over the death of small inns rooms then you may get a solution the final vote the wrong kind of war and even in some cases the bill also so I shall not to read or is diseases in the name of contributors I would just say that anonymous less also some resorts which have been obtained when you conceded the periodic there move not necessary .period but stated that the list do not indicate at infinity my idea the screamed and ducked out new and also by you and of the year and and then wellington shown different cases that say for instance for the punitive cautioned downtown you over a socalled QB lifespan neckties take caution that all sides at you get solutions the fine over interval time flanks it's known to minus 2 while no coexistence provides a solution if I'm going to refined like sitting on the minds and so would wouldn't want to do is to try and Ogilvy assumptions grew bigger and then I'm getting the sense that you make life span a whether you should ask this question to Daniels and the I'm a free man differences in Eagles a quadratic is corresponds to quartermillion narrative and then when you would have no quarrel and requests your you get 1 already long usually Deuba during a meeting you get well that seems a square but of course has annoying at the sclerotic universalist you get can because Switzerland that's why the originators of the timing of so sudanese CSM friends which shall be working with the lead survey some operational dresses metrics areas which is a matrix 1 0 0 and then say that the a solution he upside offer aware he is reversible even on the eve when the computer volume dissolution of fine minus did to cement acting was solution computer the bank so of course it for a minute free from the quality that he fears this property holds then is the 2nd component so I must finish apparently quality any conversely you start from a cautioned there was a cynical believing she's a prime many a solution will be reversing bulletin was satisfied this quarter and he's just follows from the fact that the new regulation may be written off as a state dug signed he was the sole owner central air upside where s also property that making out geometrics but as the last on carefully topside you get something which is equal to minus F all also his and so reduce immediately from the property Net central dissolution In as of this to the means Europe I will use the property Billiton and the use of a
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37:45
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case when you the same number of terms in Boston and then want to make 2 cancelations between a longterm in the 1st Simon 1 terms if they happen In this case the air economy and so on I have to distinguished to
46:39
consent was the first one being is case when such a scenario does not have so In assume that I am not In the present games that is the case would be easier given L is beautiful to me as a 7 1 in Queens sideways and 1 since interest in this case we have to function you finish in so I must say that you are not in this case then he the permit such as dangerous he stated alongside calling its upset of Sumatra then you may ensure the a small devices the mandate saying that not only the vanish the the hell is going from real life the cost of the times and 1 person represent the Bauer minus sold integer instead the words when we are not the forming in case we should be able to divide my young that that season shall be able to use to to solve the equation we where imprisoned in the at times be out equals high infant bottles chilled it seems nearly as so of course when we make such a decision would lose some growth for all of in 1 president Clinton which means that means something the realities on the question of the week which but he doesn't matter because he said the question of the question :colon low frequencies and accusing me afford to 2 rooms in roles all the managers of these questions if of course we work with swings in effect OK so see sources the equations and we wanted to study in other cases in which exceptions in cases of Cleveland in Austria and in 1 hand and cost and was 1 as we have seen in that case is the vanish identically whatever's value of his apartment and so it can solve the equation means that the last case we use is a street properties that it was mentioned reality preservation and reversible the because combining diseasefree properties when we checked that the right side was the equation In the it shall work image in this case the computer by 1 press you to banking 9 is removing weeds and be satisfied quality thank you she said so that the remaining cases the question can be solved was just as you equals 0 and we knew the substitute which it was even we haven't been able to solve in all Casey's diseases question and that we have seen before only that something he questioned whether we want to eliminate the contributions to EU H L which of the room degree of Watergate and that in doing that we are able to get by Indian quality I wear a time and exists resulted over an interval of time incidents mines and and being there was a level at which we stop this piece of process offered in English so this concludes said was Europe and this concludes might talk which is fortunate because my kind isn't real the move is part the world the other in cancelation this is the 1st of all we have heard that the was general cases "quotation mark those of some of the money on 1 of the terms the 1 which which really are important in the sense that I imagined look closely at the frequency of knowledge and so on this 1 the general so anointed in case you know what what we need to do it was the recipients and that what 1 would like to hear from the year when the is affected the question is an infinite and then use that term so that new cannot eliminate being in its attempt for which is easier other nations correspondent terms depending on the rejection so these terms and this is Eastern's it cannot grow the vessel is lost due grow because independents dressed injections and sources of terms and you need to eliminate In view of normal form using his image and character was and so why didn't we do use approach when he she because offers wooden known the same introduced before when you pass was initially along with wouldn't know when there is a meeting condition Treasury preserve that is the point that suppress forms wooden known to the New England To foster from the old and the new known and is not something that isn't a parties with you know to do that in an turn away if you included you say Here's designed them weight of the doings at step then I'm pretty confident that we could writers would prove Indian confirmed work and Soviettrained all these conditions off a permittee and and reversible of them are in some sort of progress that work in this cities and let them our industries will remember it yet the current military also questioned costs only good news for the wonders of the soul of a Europe of personal low priority areas in the 0 0 1 "quotation mark seasonal flu hit a couple of these investments about withdrawing from the area this always always on original story you need the flexibility to revising the analysis well Mosul this relation to Hollywood Holocaust also notes of so sees usefulness forming essentially from what result said usually name which was a blind to see general Frank transatlantic function satisfying some conditions so the fact that the so the fight between the princes and kept out which was but
54:14
returned yeah so the fact that sees United's offenses that idea in front of a derivative of the order does not matter at all improved offered diseases is going home you read what what what what is important is the fact that we're going to use this function as a function of side to deepen and some cap that is essentially a nontrivial dependence and this is what the rules you have to do to the put dainty service more divided estimated ceased to say that when we evaluate Cecil what true was aquatic as only attempted tourists that then moving into the campaign you may be arranged so that Aziz lower bounce this is a sign of campaigns of all year and does not as a matter of poetry you Yukon no federal kept up and get permit yeah and you can do anything with the intent of this bill will be killed take cognizance of the good oldfashioned offices in some so and it is a amazing is a basic with With amazing stocking boat as saying that the you wanted to they treat offered terms of lower degree in married so to get there gimmick resulted you have to be created all of these aquatic tunnels and narrative I don't know it and in that case and reason that position because he sees the forces yet but the point is that they don't apparently because it's at the level of the party and 1994 which you be essentially no reasons for the move it along with the like of which also revealed this side of the they don't disparity condition the disparity condition actually we needed only to you know to go to the increases the terms and the bad terms ones for which you you you you can make conceal your French trendier and so you need only to get rid of terms offer all degree in United you need to get rid of the pubic them you know unit needed to get rid of the aquatic durable order Kostic ,comma also offers courses the problem you know what the idea except that it's not exactly the same framework will them the bill is the death knell parts of the world that is is what it is yet so you know you would get the picture it doesn't there originally published well I suppose we could but we didn't try to trace down with you really want to know is general think