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Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations

Author(s): Constantin, Peter; Kukavica, Igor; Vicol, Vlad C.

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Abstract: We consider the incompressible Euler equations on RdRd or TdTd, where d∈{2,3}d∈{2,3}. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey-class radius). (b) In Lagrangian coordinates the equations are locally well-posed in highly anisotropic spaces , e.g. Gevrey-class regularity in the label a1a1 and Sobolev regularity in the labels a2,…,ada2,…,ad. (c) In Eulerian coordinates both results (a) and (b) above are false.
Publication Date: Nov-2016
Electronic Publication Date: 3-Aug-2015
Citation: Constantin, Peter, Kukavica, Igor, Vicol, Vlad. (Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 33 (1569 - 1588. doi:10.1016/j.anihpc.2015.07.002
DOI: doi:10.1016/j.anihpc.2015.07.002
10.1016/j.anihpc.2015.07.002
ISSN: 0294-1449
EISSN: 1873-1430
Pages: 1569 - 1588
Type of Material: Journal Article
Journal/Proceeding Title: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Version: Author's manuscript



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