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arXiv · 2402.11516

Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$

Lv Cai·Ning-An Lai·Wen-Ze Su
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Abstract

This paper concerns the long time existence to the smooth solutions of the compressible Euler system with critical time dependent damping in $\R^2$. We establish the sharp lifespan estimate from below, with respect to the small parameter of the initial perturbation. For this end, the vector fields $\widehat{Z}$ (defined below) are used instead of the usual one $Z$, to get better decay for the linear error terms. This idea may also apply to the long time behavior study of nonlinear wave equations with time-dependent damping.

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Lv Cai, Ning-An Lai, Wen-Ze Su. 2024-02-18. Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$. https://arxiv.org/abs/2402.11516

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