Non existence and strong ill-posedness in H2 for the stable IPM equation
We prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small H2(R2) perturbations of the linearly stable profile −x2. A remarkable novelty of the proof is the construction of an H2 perturbation, which solves the IPM equation an...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/423208 |
| Acceso en línea: | http://hdl.handle.net/10261/423208 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105009014777&doi=10.1016%2Fj.jfa.2025.111097&partnerID=40&md5=2b99d5288a451e93287be95e8f6b1267 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-existence and strong ill-posedness Partial and anisotropic dissipation Stable IPM equations |
| Sumario: | We prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small H2(R2) perturbations of the linearly stable profile −x2. A remarkable novelty of the proof is the construction of an H2 perturbation, which solves the IPM equation and neutralizes the stabilizing effect of the background profile near the origin, where a strong deformation leading to non-existence in H2 is created. This strong deformation is achieved through an iterative procedure inspired by the work of Córdoba and Martínez-Zoroa (2022) [7]. However, several differences - beyond purely technical aspects - arise due to the anisotropic and, more importantly, to the partially dissipative nature of the equation, adding further challenges to the analysis. © 2025 The Author(s) |
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