Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations

Marco Sammartino, Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review

Abstract

This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.

Original languageEnglish (US)
Pages (from-to)433-461
Number of pages29
JournalCommunications In Mathematical Physics
Volume192
Issue number2
DOIs
StatePublished - 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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