INSTANTANEOUS GAP LOSS OF SOBOLEV REGULARITY FOR THE 2D INCOMPRESSIBLE EULER EQUATIONS
We construct solutions of the 2D incompressible Euler equations in R2 × Œ0; 1/ such that initially the velocity is in the super-critical Sobolev space H β for 1 < β < 2, but is not in H β 0 for β0 > 1 C .32‒‒β.β/.β‒1/‒21/ for any t 2 .0; 1/. These solutions are not in the Yudovich class, bu...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/389427 |
| Acceso en línea: | http://hdl.handle.net/10261/389427 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85200561855&doi=10.1215%2f00127094-2023-0052&partnerID=40&md5=49367452e692455f8c2c1a76a2d267a4 |
| Access Level: | acceso abierto |
| Palabra clave: | 2D incompressible Euler equations Gap loss of Sobolev regularity Norm inflation Strong ill-posedness |
| Sumario: | We construct solutions of the 2D incompressible Euler equations in R2 × Œ0; 1/ such that initially the velocity is in the super-critical Sobolev space H β for 1 < β < 2, but is not in H β 0 for β0 > 1 C .32‒‒β.β/.β‒1/‒21/ for any t 2 .0; 1/. These solutions are not in the Yudovich class, but they exist globally in time and they are unique in a determined family of classical solutions. © 2024 Duke University Press. All rights reserved. |
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