The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners PDF Download
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Author: Paul Godin
Publisher: American Mathematical Soc.
ISBN: 1470444216
Category : Education
Languages : en
Pages : 72
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Book Description
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.
Author: Paul Godin
Publisher: American Mathematical Soc.
ISBN: 1470444216
Category : Education
Languages : en
Pages : 72
Get Book Here
Book Description
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.
Author: Paul J. Godin
Publisher:
ISBN: 9781470464646
Category : Boundary value problems
Languages : en
Pages : 0
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Book Description
"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"--
Author: Camille Laurent
Publisher: American Mathematical Society
ISBN: 1470451387
Category : Mathematics
Languages : en
Pages : 108
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Author: Leonard Gross
Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111
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Author: Matthias Grüninger
Publisher: American Mathematical Society
ISBN: 1470451344
Category : Mathematics
Languages : en
Pages : 154
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Author: Alexander V. Kolesnikov
Publisher: American Mathematical Society
ISBN: 1470451603
Category : Mathematics
Languages : en
Pages : 78
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Author: Nuno Freitas
Publisher: American Mathematical Society
ISBN: 1470452103
Category : Mathematics
Languages : en
Pages : 105
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Author: John Voight
Publisher: American Mathematical Society
ISBN: 1470452286
Category : Mathematics
Languages : en
Pages : 142
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Author: Alessandro Andretta
Publisher: American Mathematical Society
ISBN: 1470452731
Category : Mathematics
Languages : en
Pages : 189
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Author: Alan Hammond
Publisher: American Mathematical Society
ISBN: 1470452294
Category : Mathematics
Languages : en
Pages : 131
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