TY - JOUR T1 - Stability and Unstability of the Standing Wave to Euler Equations AU - Tang , Xiuli AU - Wang , Xiuqing AU - Yang , Ganshan JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 818 EP - 838 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2016.m1425 UR - https://global-sci.org/intro/article_detail/aamm/12177.html KW - Euler Equations, Lie Group, well-posedness, saddle point. AB -

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 local solutions of the compressible Euler equation.