Control and stabilization of the incompressible Euler equation with free surface

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Video in TIB AV-Portal: Control and stabilization of the incompressible Euler equation with free surface

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Control and stabilization of the incompressible Euler equation with free surface
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The incompressible Euler equation with free surface dictates the dynamics of the interface separating the air from a perfect incompressible fluid. This talk is about the controllability and the stabilization of this equation. The goal is to understand the generation and the absorption of water waves in a wave tank. These two problems are studied by two different methods: microlocal analysis for the controllability, and study of global quantities for the stabilization (multiplier method, Pohozaev identity, hamiltonian formulation, Luke’s variational principle, conservation laws...).
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the NRC is decreasing as is inter-Korean type of the energy will be controlled by a constant thing zeal and what they forgotten to 2 right is that we want the feedback loop that since we want that to be axed is defined as a function of the dumpsite the plates of passageway it is a function of the dump site by contrast was a political problem so why do we want to make netted a decrease of course because we want to dampen end-users condition what is the reason of this condition simply because if this is true and in ages decreasing age of the smaller than the main of age but this was in 1 of the divided by 2 years into a lot of each of the which she is because of the smaller than candidacy divided by capital the agency which means that you have a dumpling whenever capital is bigger than the Of course the age of 15 will be smaller than some fraction died age of 0 which means that in fact you have exponential decay simply because you can eat their agencies age at time and blanketed the would be smaller than capital city guided by teachers it times the initial that the whenever you this browbeaten and whenever the exist on long enough tenants and value of exponential decay but isn't it which is standardization so now the question is to find a feedback loop that those to obtain this book the the 1st question is to find it did not know at a loss to dissipate imagines this can be done take full of using Yanaton and formulation yelling find minute and then there the fact felt that survived back cycles that the equation on it and they can be written under this fall did you of the died but the the analogy with respect to sign the job society but minus the date accusing energy with respect to eat up minus the extent Bridge then the the directive of the can be written in this form of cross you use a cancelation coming from the fact that the question is an Internet and gaming always spot but the line at the meeting of the G . 9 6 per so you want that this is negative to dissipate and that it was simply truce for example because the function Chi minted blinded you do that then of course be but at the end of it with the the age would be negative and this explains that the choice feedback OK this battle it is widespread In the the numerical analysis of what the wave whenever you want to dump in energy to dump doing weight in the surrounding area and the question is to understand why which is localized and goes to prove that nobody gives I am going to show you an American experiment that was amended on it is extremely easy because it is an experiment flopped in their eyes question they just the committee finalized the question because you can solve the question using for its wonderful we are going to see that it works very well here we are generating weighed by blowing each about a freeze of based on the left and we generate about the quake training that is happening to the right and right way using the dunking it is down and it was when we are able to produce cutting wasteful packaging from the left to the right and evidencing only not so much reflection I'm going for it will clearly whether this American League the next statement
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OK I know a lot about the crucial program as above we are walking in a container leasing try we paradise so we asked readers to what's a good support for the weather or integration we that and With the producer manager you can think of said that with with system of this equation did you because you have huge exuberance I didn't occupancy guy off as the exuding quotas if you want to call that solution we say that sign an existing entanglement of size 1 about China you need to pull as usual uniform estimates in its Idaho Falls this equation you divide this them by the side of the at the worksite aren't because I am assuming that he depends linearly so you see that as a damping down does not add for the studios approach a problem because in fact the ad at 10 with I have future singled out and they have to be thank but but you know you ought to take it's not stifle ought to put that in his sights set my spine is 1 of outside it's not difficult but it is not insightful find entering into a sedated because political and
which is in a much more interesting from the from my point of view he stressed that is the studies and I said that being to put something that is decreasing as excommunication because it is based on the ultimate and foundation of the question but his mind pressing supposedly energy converted to seal it is loaded the gun because the question is questioning non-local and at 1st wasted his program my motivation was To is poor firstly move on but opposed by the French factories and Michael Palin medicines for them but that's because I wanted to discuss with engineers people walking in future because I wanted on purpose to the move Michael Kennedy and I wanted to use instead is instead of walking away from the accident site walking only with integral function of eating up some function and by so doing I found the book that I will not be able to find using friendship that "quotation mark this is the important thing to remember is that the book is based only on about quantity we seek exact identity using but quantity than using 6 principles the fastest evaluation that principle for what the wave of languages so managed to use them to buy of matter which is also the principle of a quick politician affinity but I identities was ejected in a manner that we use it as far as possible consolidation loans and we and formulation as it is I use of principle and I am going to explain only this the Tobias I don't want to the with the way the thus the wet isn't a method in July insisted misstated a student discipline it is used to compute this quantity you want to computing behind diamonds in the let us consider for example the 1 you integration with Jacob condition when the wind which from date of alike you have slightest identity that can be obtained by multiplying the question by X the it's you you must abide by existing and new integrated by In time and space indictments and what do you obtained Europeans simply on in time objects you evaluated that I seek 1 1 is equal to 2 times this quantity at 99 as it's going get this is in decline in times of union by her before the wedding questions today to obtain an expression forcing the unintended Xanadu which which depends only on the bond 98 Healthways something localize it is localized on exit when 1 added and that can be neglect white neglected this intrusion is very simple this is the integrally tied in together because you working and this doesn't depend on buying this is a difference at 2 different values so when to very loud this quantity would be very large wives this 1 we have a fixed sites so can rob system so you can compare theatergoing time of energy with something which is localized what this is a keeper so the key
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weights which is a general sinking into function vanishing at both and and the ensuing were in the early Wednesday you have some degree efficiency than the whole of the pending in a very simple way and then died and subsets with this way if you neglect of attention to a simple statement you have this collection is in decline in time of the Energy blasts some dumped you I would commodities acquired to something depending on the pressure about 90 100 times an observation tower and so it would comment on the stand quickly what is QQ is a positive step so you can neglect it is budgeted you neglect because it is was a good sign this is an observation why because wine minors NO X and X minus and combo sequences you will 1 0 and Maine as that of the migrant as he was there in the direction by the choice of the weight so this is an observation it depends only on the solution need exit .period and what is interesting is that they are evidently up with which means that the identity of the same puzzling arrived equation the only dampening from the 1990 is this 1 the Pentagon about a few domain of the dating of all times extend my wife at this moment in them can be very easily compare do is imagine because a concluding 5 square this latest so that only a cubic nonlinear there is this 1 and it can be political base in energy easily provided that all effects using an infuriating non-smokers and 1 of which is the belief the neighborhood assumptions on this was commissioned an instant newspaper the quality of life of the use of chadors or in some way to make youth yes the end of the meeting was planned I know that information we did l specifically when they mention that maybe not this 1 but this 1 is very specific two-dimensional mentioned to you have to use my column that analysis In this not Delaware the city into recently was the 1 you can you can flatten the coefficient is also in the invention to to flatten the collection is something that you can do it is worse than normal for example falls disappointingly sets of assumptions for them by 2 but apart from and I wanted to do his think strikeforce teammates forward they want to raise specific two-dimensional 1 is defined exist to the different In became a disease you have to use Michael smart directions to communications and and to you have to to to do something and sending them that but there are a lot of Michael insisted you can difficulties to pull low frequency because even England that a difficult to polling low-frequency that there are some tricks that you can use in their emotional and dimension to your to do something the changes the formula the related to the change of labor journalist and a general liability in exactly the same thing for funding I question considers wedding I question with equal efficiency and if you want to move to flatten the provision of to make of that for this would generate a double although 1 which would be a collected debating which is with an imaginary coefficient which is quite weak but it is and divided it is can be conducted by saying that at the beginning of the move by using pocket that factor in the prefecture shares in such a way that agenda by about the change of venue presented to me which is the case if we you make only the change of so if you make on the agenda viable units under President and also you know the kids in the structure of the group it was not just with the amendments more than that is the sum of its cause the world of U.S. the kind of guy comes from the fact that they amusing emitted by a method to put the standardization the animal infected also welcomed the choice of the guys loss of the season in what they have not explained later out to use users inequality to post that the decision is known at some point you need much more identity and for 1 of its identity I am forced to choose going this way the the few B