Displaying similar documents to “Regularity for solutions to the Navier-Stokes equations with one velocity component regular.”

Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes

Isabelle Gallagher, Dragoş Iftimie, Fabrice Planchon (2002)

Journées équations aux dérivées partielles

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We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.

Profile decompositions and applications to Navier-Stokes

Gabriel S. Koch (2010)

Journées Équations aux dérivées partielles

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In this expository note, we collect some recent results concerning the applications of methods from dispersive and hyperbolic equations to the study of regularity criteria for the Navier-Stokes equations. In particular, these methods have recently been used to give an alternative approach to the L 3 , ∞ Navier-Stokes regularity criterion of Escauriaza, Seregin and Šverák. The key tools are profile decompositions for bounded sequences of functions in critical spaces.