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In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ()).
In according to a recent thermodynamic theory proposed by G. Grioli, we consider the growth of acceleration waves in a non viscous fluid. We determine the solutions for the growth of a plane or spherical wave advancing into the fluid in mechanical but not in thermal equilibrium.
In according to a recent thermodynamic theory proposed by G. Grioli we consider the growth of acceleration waves in a non viscous fluid. We determine the solutions for the growth of a plane or spherical wave advancing into the fluid in mechanical but not in thermal equilibrium.
Il a été établi par H. Lewy (1952) qu’une surface libre hydrodynamique qui est au moins dans un voisinage d’un point à la surface libre, est automatiquement , éventuellement dans un voisinage plus petit de . Ce résultat local est un exemple qui précédait la théorie dévelopée par D. Kinderlehrer, L. Nirenberg et J. Spruck (1977 - 79) démontrant que dans beaucoup de cas, des surfaces libres ne peuvent pas être d’une régularité arbitraire, et en particulier ils existent tels que, si la surface...
Nous considérons dans ce travail l’écoulement d’un fluide dans un canal plat avec un obstacle au fond. Cet obstacle génère une surface libre qui n’est plus horizontale, comme c’est le cas sans obstacle. Nous montrons que, dans le cas sur critique, si l’obstacle n’est pas trop élevé, il y a une solution et une seule. Nous donnons des indications pour le cas sous critique et pour le problème numérique.
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
We study here the water waves problem for uneven bottoms in a highly nonlinear regime where
the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known
that, for such regimes, a generalization of the KdV equation (somehow linked to
the Camassa-Holm equation) can be derived and justified [Constantin and Lannes,
Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is
flat. We generalize here this result
with a new class of equations taking into account...
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