The 2D compressible Euler equations in bounded impermeable domains with corners / Paul Godin.

Format:

Book

Author/Creator:

Godin, Paul, author.

Series:

Memoirs of the American Mathematical Society ; v. 1313.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1313

Language:

English

Subjects (All):

Lagrange equations--Numerical solutions.

Lagrange equations.

Boundary value problems--Numerical solutions.

Boundary value problems.

Differential equations, Hyperbolic.

Gas dynamics--Mathematics.

Gas dynamics.

Physical Description:

1 online resource (pages cm.)

Place of Publication:

Providence, RI : American Mathematical Society, [2021]

System Details:

Mode of access : World Wide Web

text file

Summary:

"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 time) 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"-- Provided by publisher.

Contents:

1. Introduction 2. Statement of the results 3. The associated linear Euler equations ($C^\infty $ coefficients) 4. Proof of Proposition 3.3 and of Proposition 3.4, and more estimates 5. The associated linear Euler equations (non-$C^\infty $ coefficients) 6. Proof of Theorem 2.1, Theorem 2.2, Remark 2.1, Remark 2.2 A. Appendix A: Properties of div, curl in 2D B. Appendix B: Some properties of functional spaces C. Appendix C: Some estimates for functions with values in Sobolev spaces

Notes:

"January 2021, volume 269, number 1313 (fourth of 7 numbers)."

Includes bibliographical references.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2021

Description based on print version record.

Other Format:

Print version: Godin, Paul, 2D compressible Euler equations in bounded impermeable domains with corners /

ISBN:

9781470464646

Access Restriction:

Restricted for use by site license.