arXiv subjects

Yanmin Mu

Publications and source records attributed to Yanmin Mu.

4 recordsLinked to original sources

arXiv2025

Global existence for the relativistic Vlasov-Poisson system in a two-dimensional bounded domain

In this paper, we prove the global existence of solutions to the relativistic Vlasov-Poisson system for general initial data in convex bounded domains of two space dimensions, assuming the specular reflection boundary conditions for the distribution density. The boundary conditions for the electric potential are considered in two cases: Neumann boundary conditions and homogeneous Dirichlet boundary conditions. The core ideas involve constructing suitable velocity lemmas and applying geometric techniques. In the two-dimensional case, it is crucial to select the arc length as the parameter of the curve and to further combine this with the Frenet-Serret formulas, enabling us to effectively describe the distribution density equation near the boundary and thus establishing a vital connection in the geometric representation.

math.AP↗

arXiv2019

Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows

In this paper, we study the three-dimensional non-isentropic compressible fluid-particle flows. The system involves coupling between the Vlasov-Fokker-Planck equation and the non-isentropic compressible Navier-Stokes equations through momentum and energy exchanges. For the initial data near the given equilibrium we prove the global well-posedness of strong solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. For the periodic domain the same global well-posedness result still holds while the convergence rate is exponential. %The proof is based on the new macro-micro decomposition and energy estimates. New ideas and techniques are developed to establish the well-posedness and large-time behavior. For the global well-posedness our methods are based on the new macro-micro decomposition and fine energy estimates, while the proofs of the optimal large-time behavior rely on the Fourier analysis of the linearized Cauchy problem and the energy-spectrum method.

math.AP↗

arXiv2015

Strong solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck equations: Global existence near the equilibrium and large time behavior

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for the fluid (fluid phase) through the friction force. The friction force depends on the density, which is different from many previous studies on kinetic-fluid models and is more physical in modeling but significantly more difficult in analysis. New approach and techniques are introduced to deal with the strong coupling of the fluid and the particles. The global well-posedness of strong solution in the three-dimensional whole space is established when the initial data is a small perturbation of some given equilibrium. Moreover, the algebraic rate of convergence of solution toward the equilibrium state is obtained. For the periodic domain the same global well-posedness result still holds while the convergence rate is exponential.

math.AP↗

arXiv2014

Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.

math.AP↗