The 2d Compressible Euler Equations In Bounded Impermeable Domains With Corners
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The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners
Author: Paul Godin
language: en
Publisher: American Mathematical Soc.
Release Date: 2021-06-21
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.
The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners
"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"--
Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations
Author: Camille Laurent
language: en
Publisher: American Mathematical Society
Release Date: 2022-04-08
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