Stability and Unstability of the Standing Wave to Euler Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we first discuss the well-posedness of linearizing equations,and then study the stability and unstability of the 3-D compressible Euler Equation,by analysing the existence of saddle point. In addition, we give the existence of localsolutions of the compressible Euler equation.