Asymptotic Analysis

We consider the compressible Navier–Stokes–Fourier–Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer Ω ϵ = ω × ( 0 , ϵ ) , where ω is a 2-D domain. The aim of this paper is to show that the weak solutions in the 3-D domain converge to the strong solution of the 2-D Navier–Stokes–Fourier–Poisson system on ω as ϵ → 0 on the time interval, where the strong solution exists. We consider two different regimes in dependence on the asymptotic behaviour of the Froude number.

In this paper, we establish compactness and existence results to a Branson–Paneitz type problem on a bounded domain of R n with Navier boundary condition.

Practical applications of semiclassical measures are tightly connected with a so called oscillatory property, prevailing leakage of information related to high frequencies. In this paper we propose a complementary, concentratory property which prevents loss of information related to low frequencies. We demonstrate that semiclassical measures attain the best performance level if both the properties are satisfied simultaneously, and address a question if this is possible to achieve for an arbitrary bounded L 2 sequence, providing a negative answer. Comparison of H-measures with semiclassical ones is presented, showing precedence of the latter for problems exhibiting just a single frequency scale. Finally, we present some (strong) compactness results based on the above properties.

We are concerned with the bosonic sector of an N = 2 supersymmetric Chern–Simons–Higgs theory in 2 + 1 dimensions. Here the gauge group is SU ( N ) × U ( 1 ) and has N f flavors of fundamental matter fields. Recently, Chen, Han, Lozano, Schaposnik showed the existence of two gauge-distinct solutions carrying the same physical energy on a two dimensional flat torus. In this paper, we find a solution which has a different asymptotic behavior from Chen, Han, Lozano, Schaposnik’s result.