On an almost sharp Liouville-type theorem for fractional Navier-Stokes equations
Chamorro, Diego (Université Paris-Saclay. Laboratoire de Mathématiques et Modélisation d'Evry)
Poggi, Bruno (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	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.
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Liouville-type theorems ; Fractional navier-stokes equations
Published in:	Publicacions matemàtiques, Vol. 69 Núm. 1 (2025) , p. 27-43 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/433259
DOI: 10.5565/PUBLMAT6912502

17 p, 390.0 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles