applied mathematics

From nonisothermal BGK to Euler Maxwellians via relative entropy

arXiv:2603.25487

summary

The paper analyzes how solutions of the nonisothermal BGK kinetic model converge to Euler Maxwellians by using a relative entropy framework, providing conditional stability estimates and strong L¹ convergence under certain moment and boundedness assumptions.

Abstract

We study the hydrodynamic limit of the nonisothermal BGK model toward Euler Maxwellians. For a prescribed sufficiently smooth Euler solution, we use relative entropy to compare a BGK solution with the corresponding Euler Maxwellian. The result is conditional: for BGK solutions satisfying a uniform sixth velocity-moment bound and uniform bounds on their macroscopic velocity, temperature, and inverse temperature, we obtain a stability estimate uniform in time. The key new ingredient is the control of an additional velocity-cubic term in the relative entropy identity. For well-prepared initial data, this yields strong convergence of the BGK solution and its local Maxwellians to the target Euler Maxwellian, together with convergence of the associated macroscopic quantities.

Topics & keywords

#hydrodynamic limit#BGK model#Euler equations#relative entropy#kinetic theory#partial differential equationsnonisothermal BGKEuler Maxwellianrelative entropy methodvelocity moment boundsL^1 convergence
From nonisothermal BGK to Euler Maxwellians via relative entropy · wovepaper