Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models

Peter Constantin, Vlad Vicol, Jiahong Wu

Research output: Contribution to journalArticle

Abstract

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at least for short time. We show that they have real analytic Lagrangian paths. More precisely, we show that as long as a solution of any of these equations is in a class of regularity that assures Hölder continuous gradients of velocity, the corresponding Lagrangian paths are real analytic functions of time. The method of proof is conceptually straightforward and general, and we address the combinatorial issues head-on.

Original languageEnglish (US)
Pages (from-to)352-393
Number of pages42
JournalAdvances in Mathematics
Volume285
DOIs
StatePublished - Nov 5 2015

Fingerprint

Fluid Model
Analyticity
Incompressible Fluid
Trajectory
Quasi-geostrophic Equations
Real Analytic Functions
Path
Porous Medium Equation
Boussinesq Equations
Euler Equations
Unique Solution
Regularity
Gradient
Model
Class

Keywords

  • Analyticity
  • Euler equations
  • Lagrangian paths
  • Surface quasi-geostrophic equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models. / Constantin, Peter; Vicol, Vlad; Wu, Jiahong.

In: Advances in Mathematics, Vol. 285, 05.11.2015, p. 352-393.

Research output: Contribution to journalArticle

Constantin, Peter ; Vicol, Vlad ; Wu, Jiahong. / Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models. In: Advances in Mathematics. 2015 ; Vol. 285. pp. 352-393.
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