Seminar Analysis: Stefano Spirito (Gran Sasso Science Institute, L’Aquila)

Artificial compressibility approximation of suitable weak solutions of incompressible Navier-Stokes equations

In this talk I will discuss the problem of the approximation of suitable weak solutions of Navier-Stokes equations in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. It is well-known that suitable weak solutions enjoy the partial regularity theorem proved in the famous paper of Caffarelli-Kohn-Nirenberg, hence they are more regular than a Leray weak solutions. However, since the uniqueness of weak solutions of Navier-Stokes is unknown we don’t know if different approximation methods lead to a suitable weak solution. I will present a recent result obtained with L. C. Berselli (University of Pisa) where we proved that weak solutions obtained by some artificial compressibility approximation are suitable. The novelty of the result is that the Navier-Stokes equations are considered in a bounded domain with Navier boundary conditions.

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