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Regular Seminar
About the notion of ancient bounded solutions in the regularity theory of solutions to Navier Stokes equation(Joint with NCTS)

Speaker Professor Chi Hin Chan
Affiliation Department of Applied Mathematics, NCTU
Date 2016-03-25
Time 16:30-18:30
Venue SA212
Abstract In this talk, we will introduce the notion of ancient bounded solutions to the incompressible Navier-Stokes equations. The notion of ancient bounded solutions, as a useful conceptual tool in the regularity analysis for solutions to the incompressible Navier-Stokes equations was introduced, for the first time, in an important paper entitled "Liouville theorems for the Navier-Stokes equations and applications" by G. Koch, N. Nadirashvili, G. Seregin, and V. Sverak. In this talk, we will first take an ancient bounded solution in the weakest possible distributional sense. This means that even the local W^{1,2} property of the solution is not assumed. Then, we will derive the local W^{1,2} property of such a very weak ancient bounded solution. In the forthcoming talk, we will then use this gained local W^{1,2} property to do a bootstrap argument in order to establish the classical smoothness property of an ancient bounded solution to the Navier-Stokes equations.

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