Analysis Seminar

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Two-Dimensional Steady Solutions of the Navier-Stokes Equations in Unbounded Domains

Speaker: Julien Guillod, Princeton University

Location: Warren Weaver Hall 1302

Date: Thursday, October 6, 2016, 11 a.m.

Synopsis:

Essentially two methods are known to analyze the stationary Navier-Stokes equations in the plane: the topological method and the perturbation method. However, the problem is supercritical similarly to the three-dimensional Cauchy problem and therefore both methods have limitations, more precisely concerning the behavior at infinity of the solutions. I will present a new method to analyze this problem. The Stokes paradox states that the linearization of the Navier-Stokes equations have no bounded solutions in general. I will explain how the nonlinearity helps to obtain bounded solutions going to zero at infinity for the full nonlinear problem.