Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations

Tsukasa Iwabuchi; Dáithí Ó hAodha

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arXiv · 2312.04811

Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations

Tsukasa Iwabuchi·Dáithí Ó hAodha

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Abstract

We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space.

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Tsukasa Iwabuchi, Dáithí Ó hAodha. 2023-12-08. Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations. https://arxiv.org/abs/2312.04811

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