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<p>In this article we study mild solutions for the forced, incompressible fractional Navier–Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the nonlinearity and the external forces. Many functional spaces can be considered, however we are mainly interested here in a critical setting which ensures the existence of global solutions. We give some examples of such critical functional spaces and we discuss their relationship with generic external forces.</p>

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Some general external forces and critical mild solutions for the fractional Navier–Stokes equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月11日

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  • Diego Chamorro,
  • Maxence Mansais

摘要

In this article we study mild solutions for the forced, incompressible fractional Navier–Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the nonlinearity and the external forces. Many functional spaces can be considered, however we are mainly interested here in a critical setting which ensures the existence of global solutions. We give some examples of such critical functional spaces and we discuss their relationship with generic external forces.