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

Diego Chamorro; Maxence Mansais

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arXiv · 2606.09185

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

Diego Chamorro·Maxence Mansais

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Abstract

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.

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Diego Chamorro, Maxence Mansais. 2026-06-08. Global Mild solutions for the fractional Navier-Stokes-Boussinesq equations in critical Fourier-Herz-Lorentz spaces. https://arxiv.org/abs/2606.09185

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