On the local well-posedness of the prandtl and hydrostatic euler equations with multiple monotonicity regions

Igor Kukavica, Nader Masmoudi, Vlad Vicol, Tak Kwong Wong

Research output: Contribution to journalArticle

Abstract

We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, if the initial datum u 0 is monotone on a number of intervals (on some strictly increasing, on some strictly decreasing) and analytic on the complement of these intervals, we show that the local existence and uniqueness hold. The same result is true for the hydrostatic Euler equations if we assume these conditions for the initial vorticity ω0 = ∂yu0.

Original languageEnglish (US)
Pages (from-to)3865-3890
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number6
DOIs
StatePublished - 2014

Keywords

  • Boundary layer
  • Euler equations
  • Hydrostatic balance
  • Inviscid limit
  • Navier-Stokes equations
  • Prandtl equations

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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