Long-time behavior of weak solutions for compressible Navier-Stokes equations with degenerate viscosity

Zhilei Liang

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arXiv · 2112.13406

Long-time behavior of weak solutions for compressible Navier-Stokes equations with degenerate viscosity

Zhilei Liang

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Abstract

The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly positive from below and above after a finite period of time. Moreover, higher velocity regularity is obtained via a parabolic type iteration technique. Since then the weak solution conserves its energy equality, and decays exponentially to the equilibrium in $L^{2}$-norm as time goes to infinity. In addition, assume that the initial momentum is zero, the exponential decay rate is derived for the derivative functions, and the weak solution becomes a strong one in two dimensional space.

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Zhilei Liang. 2021-12-26. Long-time behavior of weak solutions for compressible Navier-Stokes equations with degenerate viscosity. https://arxiv.org/abs/2112.13406

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