On Uniqueness For The Three-Dimensional Vlasov-Navier-Stokes System
D Han-Kwan (LMJL, CNRS, Nantes Univ), \'E Miot (IF, CNRS, UGA), A Moussa (LJLL (UMR\_7598), CNRS, UFR 929), I Moyano (LJAD, CNRS, UniCA)
TL;DR
This paper proves the uniqueness of solutions to the 3D Vlasov-Navier-Stokes system under certain velocity conditions, extending previous classes and providing stability estimates.
Contribution
It establishes uniqueness for Leray solutions when the fluid velocity is in the Cannone-Meyer-Planchon class, surpassing the Osgood class.
Findings
Uniqueness of Leray solutions under new velocity class
Stability estimates for solutions in this setting
Extension beyond traditional Osgood class
Abstract
We study the problem of uniqueness of Leray solutions to the three-dimensional Vlasov-Navier-Stokes system. We establish uniqueness whenever the fluid velocity field belongs to the Cannone-Meyer-Planchon class, which allows to go beyond the Osgood uniqueness class. A stability estimate in this setting is also provided.
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Taxonomy
TopicsNavier-Stokes equation solutions · Gas Dynamics and Kinetic Theory · Stability and Controllability of Differential Equations