Global well-posedness and asymptotic behavior for Navier–Stokes–Coriolis equations in homogeneous Besov spaces

Article type: Research Article

Authors: Ferreira, Lucas C.F.^{a; *} | Angulo-Castillo, Vladimir^{b; **}

Affiliations: [a] IMECC-Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, CEP 13083-859, Campinas, SP, Brazil | [b] Departamento de Matemáticas, Universidad Nacional de Colombia – Sede Orinoquia, Kilometro 9 vía a Caño Limón, Arauca, Colombia

Correspondence: [*] Corresponding author. E-mail: lcff@ime.unicamp.br.

Note: [**] E-mail: vladimirangulo01@gmail.com.

Abstract: We are concerned with the 3D-Navier–Stokes equations with Coriolis force. Existence and uniqueness of global solutions in homogeneous Besov spaces are obtained for large speed of rotation. In the critical case of the regularity, we consider a suitable initial data class whose definition is based on the Stokes–Coriolis semigroup and Besov spaces. Moreover, we analyze the asymptotic behavior of solutions in that setting as the speed of rotation goes to infinity.

Keywords: Navier–Stokes equations, Coriolis force, global well-posedness, asymptotic behavior, Besov spaces

DOI: 10.3233/ASY-181496

Journal: Asymptotic Analysis, vol. 112, no. 1-2, pp. 37-58, 2019