Recent progress in proving stability of traveling waves in the 1D Navier-Stokes equations using rigorous computations

Abstract: We discuss recent progress developing and applying rigorous computation to prove stability of traveling waves in the 1D Navier-Stokes equation. In particular, we talk about rigorous computation of the Evans function, an analytic function whose zeros correspond to eigenvalues of the linearized PDE problem. Nonlinear stability results by Zumbrun and collaborators show that the underlying traveling waves are stable if there are no eigenvalues in the right half of the complex plane. Thus one may use rigorous computation of the Evans function to prove nonlinear-orbital stability of traveling waves.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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