Well-posedness Of The IBVP For Euler Equations With Damping

In this paper we focus on the small perturbation problem to the 2-D Euler equa-tion with damping.(especially under the assumption -r < s < 0). [1] have alreadydone some work under the assumption 0 < s < r,in that case,one proper bound-ary condition will be ennough.In this paper there will be a lot of difference from theboundary conditions and the energy estimates.Here,we first diagonalized the problemand then we try to give out the proper two boundary conditions, then we prove theglobal existence of classical solution to the IBVP of the 2-D Euler equation by themethod of energy estimates.