| Abstract: |
| We consider the one-dimensional 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 wave solutions, known as shock profiles. In this talk, we study the stability of these shock profiles. Our analysis is based on the pointwise semigroup method, which combines spectral analysis with Green`s function estimates. We first establish the spectral stability of the shock profiles. Building upon this, we derive pointwise bounds on the Green`s function for the associated linearized problem, which yield linear and nonlinear asymptotic orbital stability. |
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