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 …

Computer-assisted proofs in PDE: a survey | SeMA Journal Skip to main content Springer
Nature Link Account Menu Find a journal Publish with us Track your research Search Cart 1.Home …

Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …

We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving
local existence, global results for small initial data in the super-critical case, decay of L p …

Global well-posedness for the critical 2D dissipative quasi-geostrophic equation Page 1 DOI:
10.1007/s00222-006-0020-3 Invent. math. 167, 445–453 (2007) Global well-posedness for …

We study solutions to the 2D quasi-geostrophic (QGS) equation ∂ θ ∂ t+ u ⋅ ∇ θ+ κ (-Δ)^ α
θ= f and prove global existence and uniqueness of smooth solutions if α∈(12,1; weak …

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

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators,
that are general, robust, and versatile. We use these nonlinear bounds to provide …

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 …

Aimed at graduate students, researchers and academics in mathematics, engineering,
oceanography, meteorology and mechanics, this text provides a detailed introduction to the …