Energy Conservation For The Weak Solutions To The Three-dimensional Magnetohydrodynamic Equations Of Viscous Non-resistive Fluids In A Bounded Domain

In this thesis,we mainly study the energy conservation for the weak solutions to the three-dimensional magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain.Inspired by the paper[6],we use the global mollification method to obtain the energy equation.The difficulty is that the weak solutions of the magnetohydrodynamic equations of viscous non-resistive fluids do not satisfy (?).In order to obtain the energy equality,we propose a new condition for H:▽H ∈Lp1(0,T;Lq1(Ω)),p1=4p/3p-4,q1=4q/3q-4,q≥4,q≥6 and H ∈ Lt4Lx4.Under these conditions,p1∈(4/3,2],q1∈(4/3,12/7].The regularity of H is weaker than ▽H∈Lt2Lx2.The study consists of two parts.In the first part,the energy conservation for the weak solutions to the compressible three-dimensional magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain is proved under the conditions:0≤ρ≤(?)<∞,▽(?)∈ Lt∞ Lx2,u∈LtpLxq,p≥4,q≥6,H ∈ Lt4Lx4,▽H ∈Ltp1Lxq1,p1=4p/3p-4,q1=4q/3q-4.The proof is shown in Chapter 3.In the second part,the energy conservation for the weak solutions to the incompressible three-dimensional magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain is proved under the conditions:P ∈ Lt2 Lx2,v ∈ Ltp Lxq,p≥4,q≥6,b∈Lt4Lx4,▽b ∈Ltp1 Lxq1,p1=4p/3p-4,q1=4q/3q-4.The proof is shown in Chapter 4.