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

doi:10.1137/140956440

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

Mathematics

Research output: Contribution to journal › Article › peer-review

74 Scopus citations

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 language	English (US)
Pages (from-to)	3865-3890
Number of pages	26
Journal	SIAM Journal on Mathematical Analysis
Volume	46
Issue number	6
DOIs	https://doi.org/10.1137/140956440
State	Published - 2014

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

Keywords

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

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10.1137/140956440

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

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.",

keywords = "Boundary layer, Euler equations, Hydrostatic balance, Inviscid limit, Navier-Stokes equations, Prandtl equations",

author = "Igor Kukavica and Nader Masmoudi and Vlad Vicol and Wong, {Tak Kwong}",

note = "Publisher Copyright: {\textcopyright} 2014 Society for Industrial and Applied Mathematics.",

year = "2014",

doi = "10.1137/140956440",

language = "English (US)",

volume = "46",

pages = "3865--3890",

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T1 - On the local well-posedness of the prandtl and hydrostatic euler equations with multiple monotonicity regions

AU - Kukavica, Igor

AU - Masmoudi, Nader

AU - Vicol, Vlad

AU - Wong, Tak Kwong

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Boundary layer

KW - Euler equations

KW - Hydrostatic balance

KW - Inviscid limit

KW - Navier-Stokes equations

KW - Prandtl equations

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DO - 10.1137/140956440

M3 - Article

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SN - 0036-1410

VL - 46

SP - 3865

EP - 3890

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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