On dispersive effect of the Coriolis force for the stationary Navier–Stokes equations

Abstract

The dispersive effect of the Coriolis force for the stationary and non-stationary Navier-Stokes equations is investigated. Existence of a unique solution is shown for arbitrary large external force provided the Coriolis force is large enough. In addition to the stationary case, counterparts of several classical results for the nonstationary Navier-Stokes problem have been proven. The analysis is carried out in a new framework of the Fourier-Besov spaces.

Global existence of the two-dimensional QGE with sub-critical dissipation

“…Several examples of spaces with definition based on Fourier transform and containing singular data with infinite L 2 -norm have been used to study well-posedness of PDEs of parabolic, elliptic and dispersive types. The reader is referred to [4][5][6]19,12,15,17,2,13] and their references. Our local and global existence results read as follows.…”

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

“…was proved by Konieczny and Yoneda [18]. Iwabuchi and Takada [15] obtained the uniform global well-posedness with small initial velocity in the Fourier-BesovḞ B…”

Dispersive Effect of the Coriolis Force and the Local Well-Posedness for the Navier-Stokes Equations in the Rotational Framework

“…On the other hand, Giga, Inui, Mahalov and Saal [14] established the uniform global solvability of (NSC) for small initial velocity in FM for all l > 0, where u l 0 ðxÞ :¼ lu 0 ðlxÞ. In this direction, Hieber and Shibata [15] and Konieczny and Yoneda [18] obatained the uniform global solvability of (NSC) in the Sobolev space H 1=2 ðR 3 Þ and the Fourier-Besov space _ FB FB 2À3=p p; y ðR 3 Þ with 1 < p c y, respectively. For the global well-posedness for (NSC) with W ¼ 0 in the scaling invariant spaces, we refer to Fujita and Kato [9], Kato [16], Kozono and Yamazaki [19], Koch and Tataru [17], Germain [10], Bourgain and Pavlović [5] and Yoneda [22].…”