eBook ISBN:  9781470449216 
Product Code:  MEMO/256/1229.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 
eBook ISBN:  9781470449216 
Product Code:  MEMO/256/1229.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 256; 2018; 108 ppMSC: Primary 35; 76
This memoir is devoted to the proof of a wellposedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for twodimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to \(L^2\).
The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the waterwaves system, namely Strichartz estimates, to control these Hölder norms.

Table of Contents

Chapters

1. Introduction

2. Strichartz estimates

3. Cauchy problem

A. Paradifferential calculus

B. Tame estimates for the DirichletNeumann operator

C. Estimates for the Taylor coefficient

D. Sobolev estimates

E. Proof of a technical result


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This memoir is devoted to the proof of a wellposedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for twodimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to \(L^2\).
The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the waterwaves system, namely Strichartz estimates, to control these Hölder norms.

Chapters

1. Introduction

2. Strichartz estimates

3. Cauchy problem

A. Paradifferential calculus

B. Tame estimates for the DirichletNeumann operator

C. Estimates for the Taylor coefficient

D. Sobolev estimates

E. Proof of a technical result