Long-time solvability for the 2D inviscid Boussinesq equations with borderline regularity and dispersive effects

Article type: Research Article

Authors: Angulo-Castillo, V.^a | Ferreira, L.C.F.^{b; *} | Kosloff, L.^b

Affiliations: [a] Department of Mathematics, Campus Orinoquia, National University of Colombia, Kilómetro 9 vía a Caño Limón, Arauca, Colombia | [b] IMECC-Department of Mathematics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas-SP, Brazil

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We are concerned with the long-time solvability for 2D inviscid Boussinesq equations for a larger class of initial data which covers the case of borderline regularity. First we show the local solvability in Besov spaces uniformly with respect to a parameter κ associated with the stratification of the fluid. Afterwards, employing a blow-up criterion and Strichartz-type estimates, the long-time solvability is obtained for large κ regardless of the size of initial data.

Keywords: Boussinesq equations, Convection problem, Long-time solvability, Dispersive effects, Besov spaces, Borderline regularity

DOI: 10.3233/ASY-231879

Journal: Asymptotic Analysis, vol. 137, no. 1-2, pp. 53-84, 2024