The 2D compressible Euler equations in bounded impermeable domains with corners - Collections

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The 2D compressible Euler equations in bounded impermeable domains with corners

Responsibility	Paul Godin
Creator	Godin, Paul
Language	English (英語)
Publisher	American Mathematical Society
Year	2021-
Place	Providence, RI, Rhode Island
Relation	Series Memoirs of the American Mathematical Society ; number 1313
Abstract	"We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in ti...me) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces"--show more
Table of Contents	Statement of the results The associated linear Euler equations (C[infinity] coefficients) Proof of proposition 3.3 and of proposition 3.4, and more estimates The associated linear Euler equations (non-C[infinity] coefficients) Proof of theorem 2.1, theorem 2.2, remark 2.1, remark 2.2.
View fulltext	Full text available from Memoirs of the American Mathematical Society

Record ID	4783646
Subject	QA911
	532/.05
	Lagrange equations
	Boundary value problems
	Differential equations, Hyperbolic.
	Gas dynamics
	Partial differential equations -- Partial differential equations of mathematical physics and other areas of application -- Euler equations.
	Fluid mechanics -- Compressible fluids and gas dynamics, general -- Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics.
	Partial differential equations -- Hyperbolic equations and systems -- Initial-boundary value problems for first-order hyperbolic equations.
	Partial differential equations -- Hyperbolic equations and systems -- Nonlinear first-order hyperbolic equations.
SSID	ssj0002456649
LCCN	2021016988
eISBN	9781470444211[1470444216]
XISBN	9781470464646[1470464640]
Notes	"January 2021, volume 269, number 1313 (fourth of 7 numbers)."
Created Date	2022.05.12
Modified Date	2022.05.12