On an almost sharp Liouville-type theorem for fractional Navier-Stokes equations
We investigate existence, Liouville-type theorems, and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power (-∆) α 2 with 0 < α < 2. By applying a fixed-point argument, weak solut...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:304449 |
| Acceso en línea: | https://ddd.uab.cat/record/304449 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6912502 |
| Access Level: | acceso abierto |
| Palabra clave: | Liouville-type theorems Fractional navier-stokes equations |
| Sumario: | We investigate existence, Liouville-type theorems, and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power (-∆) α 2 with 0 < α < 2. By applying a fixed-point argument, weak solutions can be obtained in the Sobolev space H˙α2 (R3) and if we add an extra integrability condition, stated in terms of Lebesgue spaces, then we can prove for some values of α that the zero function is the unique smooth solution. The additional integrability condition is almost sharp for 3/5 < α < 5/3. Moreover, in the case 1 < α < 2 a gain of regularity is established under some conditions, although the study of regularity in the regime 0 < α ≤ 1 seems for the moment to be an open problem. |
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