ABSTRACT

In this talk, I will discuss with the transverse spectral instability of the one-dimensional sufficiently small and periodic traveling wave solutions of the (2+1)-dimensional Euler-Korteweg system. We show that these waves are transversely unstable with respect to two-dimensional periodically mean-zero perturbations that are periodic in both directions with long wavelength in the transverse direction. We perform a detailed spectral analysis of the linearized problem associated to the above mentioned perturbations, and derive a instability criterion which depends on the wave number k of the longitudinal waves. It is a joint work with Robin Ming Chen and Lili Fan.