Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

By D. Chamorro, O. Jarr'in, P. Lemari'e-Rieusset. Annales de l'Institut Henri Poincare. Analyse non linéar, 2018

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Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations and under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution U = 0 is the unique solution. This type of results are known as Liouville theorems.

Subfields: Applied Mathematics, Control and Systems Engineering

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