Regularity and dynamics of weak solutions for one-dimensional compressible Navier-Stokes equations with vacuum
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909763682435072 |
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| author | Tan, Jin Wang, Yan-Lin Zhang, Lan |
| author_facet | Tan, Jin Wang, Yan-Lin Zhang, Lan |
| contents | In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial boundary value problem of one-dimensional CNS with general initial data and vacuum. The core of our proof is a global in time a priori estimate for one-dimensional CNS that holds for any $H^1$ initial velocity and bounded initial density not necessarily strictly positive: it could be a density patch or a vacuum bubble. We also establish that the velocity and density decay exponentially to equilibrium. As a by-product, we obtain the quantitative dynamics of aforementioned two vacuum states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity and dynamics of weak solutions for one-dimensional compressible Navier-Stokes equations with vacuum Tan, Jin Wang, Yan-Lin Zhang, Lan Analysis of PDEs In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial boundary value problem of one-dimensional CNS with general initial data and vacuum. The core of our proof is a global in time a priori estimate for one-dimensional CNS that holds for any $H^1$ initial velocity and bounded initial density not necessarily strictly positive: it could be a density patch or a vacuum bubble. We also establish that the velocity and density decay exponentially to equilibrium. As a by-product, we obtain the quantitative dynamics of aforementioned two vacuum states. |
| title | Regularity and dynamics of weak solutions for one-dimensional compressible Navier-Stokes equations with vacuum |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.01196 |