The Landau Equation With Inflow Boundary Conditions

In the kinetic theory,the Landau equation is one of the basic models that describes the motion of particles in a rarefied gas.There is a large literature on the mathematical study of the Landau equation,and one important topic is to construct the global well-posedness of the Landau equation in different function spaces.However,it is still an open problem to find the minimum regularity function space where the global unique solution of the Landau equation near the Maxwell equilibrium state can be established.This thesis is concerned with the inflow boundary value problem of the Landau equation in a finite channel.By using the elementary energy method,a global strong solution is established for the corresponding problem in a new Lebesgue function spaceL_T^∞H_x¹ ₁H_x ² L_v².Moreover,the large time behaviors and the regularity propagation of the solution are also obtained.