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Nonlinear Partial Differential Equations

Date: November 10, 2017

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Luan T. Hoang, Texas Tech University


Title: Nonlinear PDEs (joint with Mathematical Physics Seminar)


Title: Large-time asymptotic expansions for solutions of Navier-Stokes equations

Abstract: We study the long-time behavior of solutions to the three-dimensional Navier-Stokes equations of viscous, incompressible fluids with periodic boundary conditions. The body forces decay in time either exponentially or algebraically. We establish the asymptotic expansions of Foias-Saut-type for all Leray-Hopf weak solutions. If the force has an asymptotic expansion, as time tends to infinity, in terms of exponential functions or negative-power functions, then any weak solution admits an asymptotic expansion of the same type. Moreover, when the force's expansion holds in Gevrey spaces, which have much stronger norms than the Sobolev spaces, then so does the solution's expansion. This extends the previous results of Foias and Saut in Sobolev spaces for the case of potential forces.