17 Pages
English
Gain access to the library to view online
Learn more

Cauchy problem for viscous shallow water equations Weike WANG

Gain access to the library to view online
Learn more
17 Pages
English

Description

Cauchy problem for viscous shallow water equations Weike WANG ? Department of Mathematics, Shanghai Jiao Tong University 200030 Shanghai, China Chao-Jiang XU Mathematiques UMR 6085, Universite de Rouen 76821 Mont Saint Aignan, France Abstract : In this paper, we study the Cauchy problems for viscous shallow water equations. We work in the Sobolev spaces of index s > 2, we obtain the local solutions for any initial data, and global solution for small initial data. Key words Shallow water equation, Littlewood-Paley decomposition, global solution. A.M.S. Classification 35Q, 76D 1 Introduction We consider in this work the Cauchy problems for viscous shallow water equations as follows: h(ut + (u · ?)u)? ?? · (h?u) + h?h = 0, (1.1) ht + div(hu) = 0, (1.2) u|t=0 = u0, h|t=0 = h0; (1.3) where h(x, t) is the height of fluid surface, u(x, t) = (u1(x, t), u2(x, t))t is the horizontal velocity field, x = (x1, x2) ? R2, and 0 < ? < 1 is the viscous coefficients. The equations form a quasi-linear hyperbolic-parabolic system.

  • called sobolev constant

  • sobolev space con

  • sobolev space

  • small initial

  • cauchy problem

  • using method

  • ?g1 ?

  • ?2 ≤


Subjects

Informations

Published by
Reads 7
Language English

Exrait