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Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces (2503.16362v1)
Published 20 Mar 2025 in math.AP
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}(R3) but continuously included in \dot{B}{-1}_{\infty,infty}(R3).