Open problems concerning the Holder continuity of the direction of\n vorticity for the Navier-Stokes equations

2016/04/27 by H. Beirão da Veiga, da Veiga, Hugo Beirao
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1604.08083

openalex publication_date 2016/04/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In these notes we consider solutions u to the evolution three dimensional\nNavier-Stokes equations in the whole space. Set w= curl u, the vorticity of u.\nOur study concerns mainly the relation between Holdercontinuity assumptions on\nthe direction of the vorticity and induced space-time integrability regularity\nresults for w. We discuss some related open problems, consistent with our\ncalculations. We hope that our approach should help readers interesting in\ncarrying on the investigation.\n

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