Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit

Yasunori Maekawa

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We consider the Navier-Stokes equations for viscous incompressible ows in the half plane under the no-slip boundary condition. In this paper we first establish a solution formula for the vorticity equations through the appropriate vorticity formulation. The formula is then applied to establish the asymptotic expansion of vorticity fields at υ → 0 that holds at least up to the time cv1/3, where υ is the viscosity coefficient and c is a constant. As a consequence, we get a natural sufficient condition on the initial data for the vorticity to blow up at the inviscid limit, together with explicit estimates.

Original languageEnglish
Pages (from-to)101-146
Number of pages46
JournalAdvances in Differential Equations
Volume18
Issue number1-2
Publication statusPublished - 2013 Sep 19

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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