Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system

被引：19

作者：

Han-Kwan, Daniel ^{[1
]}

Miot, Evelyne ^{[2
]}

Moussa, Ayman ^{[3
]}

Moyano, Ivan ^{[4
]}

机构：

[1] Ecole Polytech, CNRS, Ctr Math Laurent Schwartz UMR 7640, F-91128 Palaiseau, France

[2] Univ Grenoble Alpes, CNRS, Inst Fourier UMR 5582, BP 74, F-38402 St Martin Dheres, France

[3] Univ Paris Diderot SPC, Sorbonne Univ, CNRS, UMR 7598,Lab Jacques Louis Lions, F-75005 Paris, France

[4] Univ Cambridge, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2020年 / 36卷 / 01期

关键词：

Fluid-particle flows; weak solutions; uniqueness; fluid-kinetic systems; GLOBAL EXISTENCE; EQUATIONS; REGULARITY;

D O I：

10.4171/RMI/1120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a uniqueness result for weak solutions to the Vlasov-Navier-Stokes system in two dimensions, both in the whole space and in the periodic case, under a mild decay condition on the initial distribution function. The main result is achieved by combining methods from optimal transportation (introduced in this context by G. Loeper) with the use of Hardy's maximal function, in order to obtain some fine Wasserstein-like estimates for the difference of two solutions of the Vlasov equation.

引用

页码：37 / 60

页数：24

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