arXiv subjects

Maxence Mansais

Publications and source records attributed to Maxence Mansais.

3 recordsLinked to original sources

arXiv2026

Global Mild solutions for the fractional Navier-Stokes-Boussinesq equations in critical Fourier-Herz-Lorentz spaces

We construct here global in time mild solutions to the forced fractional Navier-Stokes-Boussinesq system in some critical Fourier-Herz spaces which will be based on Lorentz norms in the time and the frequency variables. For the initial data and for the external force we will consider Fourier-Besov spaces that will also be based on Lorentz spaces. Moreover, we will show, by performing a separate study of the velocity field and the temperature, that it is possible to consider one of the largest functional space -in the Fourier-Besov-Lorentz framework-for the initial velocity field.

math.AP↗

arXiv2025

Global mild solutions in a critical setting for a forced fractional Boussinesq system

We study here mild solutions for the forced, incompressible fractional Boussinesq system. Under suitable estimates for the terms involved (in an adapted functional framework) we can invoque a fixed point argument in order to obtain mild solutions. Although many functional spaces can be considered, we are interested here in a critical setting which ensures the existence of global solutions and we will work in particular with parabolic Morrey spaces which provide one of the largest critical functional frameworks available for constructing mild solutions for the fractional Boussinesq equations.

math.AP↗

arXiv2025

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

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.

math.AP↗