Asymptotic Analysis - Volume 109, issue 3-4

Authors: Ducomet, Bernard | Caggio, Matteo | Nečasová, Šárka | Pokorný, Milan

Article Type: Research Article

Abstract: 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. Show more

Keywords: Navier–Stokes–Fourier–Poisson system, weak solution, entropy, rotation, accretion disk, thin domains, dimension reduction, strong solution

DOI: 10.3233/ASY-181472

Citation: Asymptotic Analysis, vol. 109, no. 3-4, pp. 111-141, 2018

Authors: Abdelhedi, Wael | Chtioui, Hichem | Hajaiej, Hichem

Article Type: Research Article

Abstract: 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.

Keywords: Nonlinear elliptic PDE, critical exponent, lack of compactness, critical points at infinity

DOI: 10.3233/ASY-181473

Citation: Asymptotic Analysis, vol. 109, no. 3-4, pp. 143-170, 2018

Authors: Erceg, Marko | Lazar, Martin

Article Type: Research Article

Abstract: 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. Show more

Keywords: Semiclassical measures, H-measures, oscillatory sequence, concentratory sequence, characteristic scale, Kolmogorov–Riesz compactness theorem

DOI: 10.3233/ASY-181474

Citation: Asymptotic Analysis, vol. 109, no. 3-4, pp. 171-192, 2018

Authors: Kwon, Ohsang | Lee, Youngae

Article Type: Research Article

Abstract: 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.

Keywords: Non-Abelian Chern–Simons–Higgs vortices, nonlinear elliptic PDE system, doubly periodic solutions

DOI: 10.3233/ASY-181490

Citation: Asymptotic Analysis, vol. 109, no. 3-4, pp. 193-207, 2018