Some Liouville-type Theorems For Stationary Magneto-micropolar Fluid Equations

The Liouville problem is an important problem in the theoretical study of stationary fluid dynamics equations,recently it has attracted a lot of attention.In this thesis,we devote to giving two types of Liouville theorems for 3D stationary incompressible magneto-micropolar fluid equations in Lebesgue and Lorentz spaces,respectively.This thesis is divided into two parts.In the first part,we prove the Liouvilletype theorem for 3D stationary incompressible Hall-magneto-micropolar fluid equations in Lebesgue spaces.Specifically,let(u,ω,b)be a smooth solution to the 3D stationary incompressible Hall-magneto-micropolar fluid equations,we can prove u=ω=b=0 under the condition that the velocity(u,ω)∈ Lp(R3)with 2 ≤p≤9/2 and the magnetic field b ∈ Lq(R3)with 3<q≤9/2.Compared with the previous results,the range of q is expanded from 4≤q≤9/2 to 3<q≤9/2 in this chapter.In the second part,we prove the Liouville-type theorem for 3D stationary incompressible magneto-micropolar fluid equations in Lorentz spaces.Specifically,we can prove u=ω=b=0 under the condition that(u,ω,b)∈ Lr,q(R3)with 3 ≤r<9/2 and 3<q<∞.