Stationary Navier-Stokes Equations with Critically Singular External\n Forces: Existence and Stability Results

2011/11/11 by Tuoc Phan, Van Phan, Tuoc, Nguyen Cong Phuc +1 · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1111.2787

Abstract

We show the unique existence of solutions to stationary Navier-Stokes\nequations with small singular external forces belonging to a critical space. To\nthe best of our knowledge, this is the largest critical space that is available\nup to now for this kind of existence. This result can be viewed as the\nstationary counterpart of the existence result obtained by H. Koch and D.\nTataru for the free non-stationary Navier-Stokes equations with initial data in\nBMO^-1. The stability of the stationary solutions in such spaces is also\nobtained by a series of sharp estimates for resolvents of a singularly\nperturbed operator and the corresponding semigroup.\n

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

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