Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area

In this work we consider the linear stability of a sub-to-super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. This sub-to-super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory. The main result of this work is to show that the sub-to-super inviscid transonic stationary wave is physically relevant in the sense that it is L∞ linearly stable on any bounded space interval as long as its velocity is greater than 1/ √ 2 of the sound speed. ∗Department of Mathematics, National Central University, Chung-Li 32001, Taiwan, Email: [email protected]. Partially supported by National Science Council of Taiwan. †Department of Mathematics, National Central University, Chung-Li 32001, Taiwan, Email: [email protected]. Partially supported by National Science Council and NCTS of Taiwan. ‡Department of Mathematics, National Central University, Chung-Li 32001, Taiwan, Email: [email protected]. §Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA, E-mail: [email protected]. Partially supported by National Science Foundation of USA Grant DMS0807327 and University of Kansas GRF 2301264-003.