Abstract: In this talk, we consider the Navier-Stokes-Poisson (NSP) system which describes the dynamics of positive ions in a collision-dominated plasma. The NSP system admits a one-parameter family of smooth traveling waves, known as shock profiles. I will present my research on the stability of the shock profiles. Our analysis is based on the pointwise semigroup method, a spectral approach. We first establish spectral stability. Based on this, we obtain pointwise bounds on the Green's function for the associated linearized problem, which yield linear and nonlinear asymptotic orbital stability.
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