Displaying similar documents to “Dispersive and Strichartz estimates for the wave equation in domains with boundary”

Resolvent estimates and the decay of the solution to the wave equation with potential

Vladimir Georgiev (2001)

Journées équations aux dérivées partielles

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We prove a weighted L ∞ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.

Low regularity Cauchy theory for the water-waves problem: canals and swimming pools

T. Alazard, N. Burq, C. Zuily (2011)

Journées Équations aux dérivées partielles

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The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [, ], after suitable para-linearizations, the system can be arranged...

A minicourse on global existence and blowup of classical solutions to multidimensional quasilinear wave equations

Serge Alinhac (2002)

Journées équations aux dérivées partielles

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The aim of this mini-course is twofold: describe quickly the framework of quasilinear wave equation with small data; and give a detailed sketch of the proofs of the blowup theorems in this framework. The first chapter introduces the main tools and concepts, and presents the main results as solutions of natural conjectures. The second chapter gives a self-contained account of geometric blowup and of its applications to present problem.