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arXiv · 2503.16362

Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces

Leithold L. Aurazo-Alvarez·Wladimir Neves
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Abstract

In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm Besov-Lebesgue spaces and also mixed-norm Fourier-Besov-Lebesgue spaces. The main tools are the Bernstein's type inequalities, Bony's paraproduct to estimate the bilinear term and a fixed point scheme in order to get the well-posedness. Our results complement and cover previous and recents result on (Fourier-)Besov spaces and, for instance, provide a new class of initial data possibly not included in BMO^{-1}(R^3) but continuously included in \dot{B}^{-1}_{\infty,infty}(R^3).

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Leithold L. Aurazo-Alvarez, Wladimir Neves. 2025-03-20. Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces. https://arxiv.org/abs/2503.16362

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