Well-Posedness and Stability for the Viscous Primitive Equations of Geophysics in Critical Fourier-Besov-Morrey Spaces

Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type

“…The present paper is part of Ph.D thesis [3]. After concluding this work, we became aware of the preprint [2] in which the authors independently proved a well-posedness result with α = 1 similar to the one obtained here.…”

“…In this section we state the main result of this work. 2 and v 0 = (u 0 , √ gθ 0 /N ) ∈ FN s q,µ,r be such that u 0 is a divergence-free vector field and θ 0 a scalar field. Assume that α and r satisfy either the following conditions…”

Global well-posedness for the fractional Boussinesq–Coriolis system with stratification in a framework of Fourier–Besov type

“…In particular, considering the critical dissipation α = 1/2, have the well-posedness in critical Fourier-Besov-Morrey spaces for the Navier-Stokes system with critical dissipation, that is, (FNSC) with the Coriolis parameter = 0 and α = 1/2, which extends the corresponding result of [39] in Fourier-Besov spaces. Remark 3.3 By technical reasons from the employed method and estimates for the (FBCS)semigroup (2.6) (see (2.7) and Lemmas 4.1 and 4.2 below), we consider ( , N ) ∈ (R−{0}) 2 , excluding in particular = 0. However, when one deals with the rotating system (N = 0 and θ ≡ 0), the kind of space and approach considered here are consistent for any value of the parameter .…”

“…The present paper is part of Ph.D. thesis [3]. After concluding this work, we became aware of the preprint [2] in which the authors independently proved a well-posedness result with α = 1 and in a more restricted family of FN s q,μ,r -spaces, where s = 2…”