The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners
| Title | The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners PDF eBook |
| Author | Paul Godin |
| Publisher | American Mathematical Soc. |
| Pages | 72 |
| Release | 2021-06-21 |
| Genre | Education |
| ISBN | 1470444216 |
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
| Title | The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners PDF eBook |
| Author | Paul J. Godin |
| Publisher | |
| Pages | 0 |
| Release | 1900 |
| Genre | Boundary value problems |
| ISBN | 9781470464646 |
"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
| Title | Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations PDF eBook |
| Author | Camille Laurent |
| Publisher | American Mathematical Society |
| Pages | 108 |
| Release | 2022-04-08 |
| Genre | Mathematics |
| ISBN | 1470451387 |
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The Yang-Mills Heat Equation with Finite Action in Three Dimensions
| Title | The Yang-Mills Heat Equation with Finite Action in Three Dimensions PDF eBook |
| Author | Leonard Gross |
| Publisher | American Mathematical Society |
| Pages | 111 |
| Release | 2022-02-02 |
| Genre | Mathematics |
| ISBN | 1470450534 |
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Cubic Action of a Rank One Group
| Title | Cubic Action of a Rank One Group PDF eBook |
| Author | Matthias Grüninger |
| Publisher | American Mathematical Society |
| Pages | 154 |
| Release | 2022-04-08 |
| Genre | Mathematics |
| ISBN | 1470451344 |
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Local $L^p$-Brunn-Minkowski Inequalities for $p
| Title | Local $L^p$-Brunn-Minkowski Inequalities for $p PDF eBook |
| Author | Alexander V. Kolesnikov |
| Publisher | American Mathematical Society |
| Pages | 78 |
| Release | 2022-05-24 |
| Genre | Mathematics |
| ISBN | 1470451603 |
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On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves
| Title | On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves PDF eBook |
| Author | Nuno Freitas |
| Publisher | American Mathematical Society |
| Pages | 105 |
| Release | 2022-05-24 |
| Genre | Mathematics |
| ISBN | 1470452103 |
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