CONVERGENCE OF A VECTOR-BGK APPROXIMATION FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

被引：8

作者：

Bianchini, Roberta ^{[1
]}

Natalini, Roberto ^{[2
]}

机构：

[1] Ecole Normale Super Lyon, ENS Lyon, UMPA, 46 Allee Italie, F-69364 Lyon 07, France

[2] CNR, Ist Applicaz Calcolo Mauro Picone, Via Taurini 19, I-00185 Rome, Italy

来源：

关键词：

Vector-BGK model; discrete velocities; incompressible Navier-Stokes equations; conservative-dissipative form; DISCRETE KINETIC APPROXIMATION; DISSIPATIVE HYPERBOLIC SYSTEMS; FLUID DYNAMIC LIMITS; GLOBAL EXISTENCE; SMOOTH SOLUTIONS; SCHEMES;

D O I：

10.3934/krm.2019006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a rigorous convergence result for smooth solutions to a singular semilinear hyperbolic approximation, called vector-BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof deeply relies on the dissipative properties of the system and on the use of an energy which is provided by a symmetrizer, whose entries are weighted in a suitable way with respect to the singular perturbation parameter. This strategy allows us to perform uniform energy estimates and to prove the convergence by compactness.

引用

页码：133 / 158

页数：26

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