Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this
quantity is conserved along the geostrophic flow. However, in addition to potential vorticity …

This series of books forms a unique and rigorous treatise on various mathematical aspects
of fluid mechanics models. These models consist of systems of nonlinear partial differential …

The formation of strong and potentially singular fronts in a two-dimensional
quasigeostrophic active scalar is studied through the symbiotic interaction of mathematical …

The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the
evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal …

In this paper, we study the regularity of weak solution to the incompressible
magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of …

Global Well-Posedness of the Three-Dimensional Viscous Primitive Equations of Large Scale
Ocean and Atmosphere Dynamics Page 1 Annals of Mathematics, 166 (2007), 245-267 Global …

Growth in the Muskat problem Page 1 Math. Model. Nat. Phenom. 15 (2020) 7 Mathematical
Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2019021 www.mmnp-journal.org …

We develop an efficient dynamically adaptive mesh generator for time-dependent problems
in two or more dimensions. The mesh generator is motivated by the variational approach …

The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

Abstract For all ϵ> 0 ϵ> 0, we prove the existence of finite-energy strong solutions to the axi-
symmetric 3 D Euler equations on the domains {(x, y, z) ∈ R^ 3:(1+ ϵ| z|)^ 2 ≤ x^ 2+ y …