We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation ()^<i></i>/2, 0 &lt; <i></i> 1). We show in this paper that if , or with is a weak solution of the 2D quasi-geostrophic equation, then <i></i> is a classical solution in . This result improves our previous result in [18].

In this paper we study the effects of small viscosity term and the far-field boundary conditions for systems of convection-diffusion equations in the zero viscosity limit. The far-field boundary conditions are classified and the corresponding solution structures are analyzed. It is confirmed that the Neumann type of far-field boundary condition is preferred. On the other hand, we also identify a class of improperly coupled boundary conditions which lead to catastrophic reflection waves dominating the inlet in the zero viscosity limit. The analysis is performed on the linearized convection-diffusion model which well describes the behavior at the far field for many physical and engineering systems such as fluid dynamical equations and electro-magnetic equations. The results obtained here should provide some theoretical guidance for designing effective far field boundary conditions.

No abstract uploaded!

In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.

No abstract uploaded!