Local well-posedness of the $1d$ compressible Navier-Stokes system with rough data

Ke Chen; Ruilin Hu; Quoc-Hung Nguyen

Local well-posedness of the $1d$ compressible Navier-Stokes system with rough data

Analysis of PDEs 2022-06-29 v1

Authors: Ke Chen , Ruilin Hu , Quoc-Hung Nguyen

Abstract

This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic equation with piecewise continuous coefficients.

Keywords

compressible navier-stokes local well-posedness rough data parabolic equation smoothing estimates

Cite

@article{arxiv.2206.14160,
  title  = {Local well-posedness of the $1d$ compressible Navier-Stokes system with rough data},
  author = {Ke Chen and Ruilin Hu and Quoc-Hung Nguyen},
  journal= {arXiv preprint arXiv:2206.14160},
  year   = {2022}
}

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37 pages

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