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

T. Alazard; N. Burq; C. Zuily

Displaying similar documents to “Low regularity Cauchy theory for the water-waves problem: canals and swimming pools”

On the instability of solitary-wave solutions for fifth-order water wave models.

Angulo Pava, Jaime (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

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

Serge Alinhac (2002)

Journées équations aux dérivées partielles

Similarity:

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.

Dispersive and Strichartz estimates for the wave equation in domains with boundary

Oana Ivanovici (2010)

Journées Équations aux dérivées partielles

Similarity:

In this note we consider a strictly convex domain $Ω \subset ℝ^{d}$ of dimension $d \geq 2$ with smooth boundary $\partial Ω \neq \emptyset$ and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.

Painlevé analysis and similarity reductions for the magma equation.

Harris, Shirley E., Clarkson, Peter A. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Geometrical methods in hydrodynamics

Adrian Constantin (2001)

Journées équations aux dérivées partielles

Similarity:

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

Solution of the system of differential equations related to Marangoni convections in one fluid layer.

Matoog, R.T., Bukhari, Abdl-Fattah K. (2008)

APPS. Applied Sciences

Similarity:

Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems

Mihai Mariş (2010)

Journées Équations aux dérivées partielles

Similarity:

This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.