The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners

The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners
Author :
Publisher : American Mathematical Soc.
Total Pages : 72
Release :
ISBN-10 : 9781470444211
ISBN-13 : 1470444216
Rating : 4/5 (11 Downloads)

Book Synopsis The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners by : Paul Godin

Download or read book The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners written by Paul Godin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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