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arXiv · 2412.20957

Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation

Feimin Huang·Guiqin Qiu·Yi Wang·Xiaozhou Yang
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Abstract

We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation $u_t+uu_x+uu_y=\Delta u$, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve $y=\varphi(x)$, and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.

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Feimin Huang, Guiqin Qiu, Yi Wang, Xiaozhou Yang. 2024-12-30. Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation. https://arxiv.org/abs/2412.20957

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