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 Caflisch

Research output: Contribution to journalArticle

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
StatePublished - 1998

Fingerprint

Cauchy's integral theorem
half spaces
Analytic Solution
Half-space
Navier-Stokes equation
Euler
Viscosity
Navier-Stokes Equations
viscosity
Cauchy Equation
Zero
Incompressible Navier-Stokes Equations
theorems
Projection Method
Euler Equations
existence theorems
Existence Theorem
Vertical
Operator
projection

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Communications in Mathematical Physics, Vol. 192, No. 2, 1998, p. 433-461.

Research output: Contribution to journalArticle

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