Global classical solution of the Cauchy problem to 1D compressible Navier-Stokes equations with large initial data

Quansen Jiu; Mingjie Li; Yulin Ye

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arXiv · 1310.5289

Global classical solution of the Cauchy problem to 1D compressible Navier-Stokes equations with large initial data

Quansen Jiu·Mingjie Li·Yulin Ye

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Abstract

In this paper, we prove that the 1D Cauchy problem of the compressible Navier-Stokes equations admits a unique global classical solution $(ρ,\rm u)$ if the viscosity $μ(ρ)=1+ρ^β$ with $β\geq0$. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.

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Quansen Jiu, Mingjie Li, Yulin Ye. 2013-10-20. Global classical solution of the Cauchy problem to 1D compressible Navier-Stokes equations with large initial data. https://arxiv.org/abs/1310.5289

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