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

2025/03/24 by Diego Chamorro, Chamorro, Diego, Maxence Mansais +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.18450

openalex publication_date 2025/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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