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arXiv · 2101.05488

The inviscid limit of third-order linear and nonlinear acoustic equations

Barbara Kaltenbacher·Vanja Nikolić
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Abstract

We analyze the behavior of third-order in time linear and nonlinear sound waves in thermally relaxing fluids and gases as the sound diffusivity vanishes. The nonlinear acoustic propagation is modeled by the Jordan--Moore--Gibson--Thompson equation both in its Westervelt and in its Kuznetsov-type forms, that is, including quadratic nonlinearities of the type $(u^2)_{tt}$ and $ (u_t^2 + |\nabla u|^2)_t$. As it turns out, sufficiently smooth solutions of these equations converge in the energy norm to the solutions of the corresponding inviscid models at a linear rate. Numerical experiments illustrate our theoretical findings.

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Barbara Kaltenbacher, Vanja Nikolić. 2021-01-14. The inviscid limit of third-order linear and nonlinear acoustic equations. https://arxiv.org/abs/2101.05488

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