Incompressible flow in porous media with fractional diffusion
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for th...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/45190 |
| Acceso en línea: | http://hdl.handle.net/11441/45190 https://doi.org/10.1088/0951-7715/22/8/002 |
| Access Level: | acceso abierto |
| Palabra clave: | Flows in porous media |
| Sumario: | In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different cases. Moreover, we obtain the decay of the solution in Lp, for any p ≥ 2, and the asymptotic behavior is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with α ∈ (1, 2], we obtain the existence of the global attractor for the solutions in the space Hs for any s > (N/2) + 1 − α. |
|---|