Scholarlink

<p>It is well-known that the gradient of velocity, when considered in its scaling-invariant Lebesgue spaces, ensures the regularity of weak solutions to the three-dimensional incompressible Navier-Stokes equations, as established by Beirão da Veiga [<CitationRef CitationID="CR2">2</CitationRef>, <CitationRef CitationID="CR3">3</CitationRef>]. Inspired by the recent work [<CitationRef CitationID="CR43">43</CitationRef>] of the second author, and utilizing the concept of effective viscous flux, we derive certain Beirão da Veiga-type blow-up criteria for the isentropic compressible Navier-Stokes equations allowing vacuum, under the assumption of a bounded supernorm of the density. This formulation complements and extends the Ladyzhenskaya-Prodi-Serrin-type blow-up criteria to compressible viscous fluids. Notably, the velocity gradient can be replaced by the deformation tensor, and these criteria remain applicable to isentropic compressible magnetohydrodynamic equations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Beirão da Veiga type criteria for the three dimensional isentropic compressible Navier-Stokes equations

  • 期刊论文

  • 发表日期：

    2026年2月27日

查看全文
  • Yanqing Wang,
  • Yongfu Wang,
  • Yulin Ye

摘要

It is well-known that the gradient of velocity, when considered in its scaling-invariant Lebesgue spaces, ensures the regularity of weak solutions to the three-dimensional incompressible Navier-Stokes equations, as established by Beirão da Veiga [2, 3]. Inspired by the recent work [43] of the second author, and utilizing the concept of effective viscous flux, we derive certain Beirão da Veiga-type blow-up criteria for the isentropic compressible Navier-Stokes equations allowing vacuum, under the assumption of a bounded supernorm of the density. This formulation complements and extends the Ladyzhenskaya-Prodi-Serrin-type blow-up criteria to compressible viscous fluids. Notably, the velocity gradient can be replaced by the deformation tensor, and these criteria remain applicable to isentropic compressible magnetohydrodynamic equations.