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Large data oscillatory solutions of the 3D Navier-Stokes equations

PDE and Applied Math Seminar

Speaker: Walter Rusin, USC
Location: 1147 MSB
Start time: Tue, May 15 2012, 3:10PM

We consider the 3D Navier-Stokes equations in a periodic domain thus focusing on oscillatory solutions. Heuristically, as the frequency of oscillations vanishes, solutions converge to the solution of the 2.5D Navier-Stokes equations, that is equations, where the third component of velocity is propagated by the solution. We explore this phenomenon and exhibit a set of quantities and conditions which guarantee the existence of global regular solutions. The considered initial data are genuinely three-dimensional. The talk is based on joint work with Igor Kukavica.