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arXiv · 2012.12966

Asymptotic approximation of a modified compressible Navier-Stokes system

Ryan Goh·C. Eugene Wayne·Roland Welter
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Abstract

We study the long time asymptotics of a modified compressible Navier-Stokes system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a new decomposition of the momentum field into its irrotational and incompressible parts, and a new method for approximating solutions of the heat equation in terms of Hermite functions in which $n^{th}$ order approximations can be computed for solutions with $n^{th}$ order moments. We then obtain existence of solutions to the mcNS system and show that the approximation in terms of Hermite functions gives the leading order terms in the long-time asymptotics, and under certain assumptions can be evaluated explicitly.

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Ryan Goh, C. Eugene Wayne, Roland Welter. 2020-12-23. Asymptotic approximation of a modified compressible Navier-Stokes system. https://doi.org/10.1512/iumj.2023.72.9272

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