3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
speaker: Alex Mahalov (Arizona State University)abstract: In the first part of the talk, we study the 3D Navier-Stokes Equations with uniformly large initial vorticity and prove existence on infinite time intervals of regular strong solutions; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold. The global existence is proven using techniques of fast singular oscillating limits, Lemmas on restricted convolutions and the Littlewood-Paley dyadic decomposition. In the second part of the talk, we analyze regularity and dynamics of the 3D Euler equations with uniformly large initial vorticity in bounded cylindrical domains.
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