On the 3D Euler equations with Coriolis force in borderline Besov spaces

On the Axisymmetric Euler Equations with Initial Vorticity in Borderline Spaces of Besov Type

Borderline spaces of Besov type consist of tempered distributions satisfying the property that the partial sums of their B ∞,1-norm diverge in a controlled way. We prove an existence and uniqueness result for the three-dimensional axisymmetric Euler equations without swirl when initial vorticity belongs to these spaces. We also prove that for this class of solutions the vanishing viscosity limi...

The Axisymmetric Euler Equations with Vorticity in Borderline Spaces of Besov Type

Borderline spaces of Besov type consist of tempered distributions satisfying the property that the partial sums of their B ∞,1-norm diverge in a controlled way. Misha Vishik established uniqueness of solutions to the two and three-dimensional incompressible Euler equations with vorticity whose B ∞,1 partial sums diverge roughly at a rate of N logN . In two dimensions, he also established condit...

Regularity criteria for the 3D magneto-micropolar fluid equations in Besov spaces with negative indices

Shallow water equations with a complete Coriolis force and topography

This paper derives a set of two dimensional equations describing a thin inviscid fluid layer flowing over topography in a frame rotating about an arbitrary axis. These equations retain various terms involving the locally horizontal components of the angular velocity vector that are discarded in the usual shallow water equations. The obliquely rotating shallow water equations are derived both by...

The Generalized Incompressible Navier-Stokes Equations in Besov Spaces

This paper is concerned with global solutions of the generalized Navier-Stokes equations. The generalized Navier-Stokes equations here refer to the equations obtained by replacing the Laplacian in the Navier-Stokes equations by the more general operator (−∆) with α > 0. It has previously been shown that any classical solution of the d-dimensional generalized NavierStokes equations with α ≥ 1 2 ...