Solutions of the 2D quasi-geostrophic equation in Hölder spaces Original Research Article

The 2D quasi-geostrophic equation View the MathML source∂tθ+u·∇θ+κ(-Δ)αθ=0,u=R⊥(θ) Turn MathJax on is a two-dimensional model of the 3D hydrodynamics equations. When View the MathML sourceα⩽12, the issue of existence and uniqueness concerning this equation becomes difficult. It is shown here that this equation with either κ=0κ=0 or κ>0κ>0 and View the MathML source0⩽α⩽12 has a unique local in time solution corresponding to any initial datum in the space Cr∩LqCr∩Lq for r>1r>1 and q>1q>1.