Asymptotic Analysis - Volume 113, issue 1-2

Authors: Kukavica, Igor | Xu, Fanhui

Article Type: Research Article

Abstract: We consider the stochastic Euler equations driven by the Lévy noise. We construct a unique local pathwise solution in the Sobolev space W s , p ( R d ) where s > d / p + 1 .

Keywords: Stochastic Euler equations, Lévy noise, existence

DOI: 10.3233/ASY-181505

Citation: Asymptotic Analysis, vol. 113, no. 1-2, pp. 1-27, 2019

Authors: Jleli, Mohamed | Samet, Bessem

Article Type: Research Article

Abstract: In this paper, we study, for the first time, the nonexistence of solutions to systems of parabolic differential inequalities in 2D exterior domains with Dirichlet and Neumann boundary conditions. Our obtained results complete those derived recently by Yuhua Sun [Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of R N , Pacific Journal of Mathematics. 293(1) (2018) 245–256] in the N -dimensional case, N ⩾ 3 , under Dirichlet boundary condition.

Keywords: Noexistence, systems of parabolic differential inequalities, 2D exterior domain

DOI: 10.3233/ASY-181506

Citation: Asymptotic Analysis, vol. 113, no. 1-2, pp. 29-49, 2019

Authors: Abels, Helmut | Daube, Johannes | Kraus, Christiane

Article Type: Research Article

Abstract: For the two-phase incompressible Navier–Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation.

Keywords: Fluid mechanics, Navier–Stokes equations, free boundary problems, surface tension

DOI: 10.3233/ASY-181507

Citation: Asymptotic Analysis, vol. 113, no. 1-2, pp. 51-86, 2019

Authors: Klevtsovskiy, Arsen V. | Mel’nyk, Taras A.

Article Type: Research Article

Abstract: A thin graph-like junction Ω ε ⊂ R 3 consists of several thin curvilinear cylinders that are joined through a domain (node) of diameter O ( ε ) . Here ε is a small parameter characterizing the thickness of the thin cylinders and the node. In Ω ε we consider a semilinear parabolic problem with nonlinear perturbed Robin boundary conditions both on the lateral surfaces of the cylinders and the node boundary. The purpose is to study the asymptotic behavior of …the solution u ε as ε → 0 , i.e. when the thin graph-like junction is shrunk into a graph. The passage to the limit is accompanied by special intensity factor ε α 0 in the Robin condition on the node boundary. We establish qualitatively different cases in the asymptotic behaviour of the solution depending on the value of parameter α 0 . For each case we construct the asymptotic approximation for the solution up to the second terms of the asymptotics and prove the asymptotic estimates from which the influence of the local geometric heterogeneity of the node and physical processes inside are observed. Show more

Keywords: Approximation, semilinear parabolic problem, asymptotic estimate, thin graph-like junction

DOI: 10.3233/ASY-181511

Citation: Asymptotic Analysis, vol. 113, no. 1-2, pp. 87-121, 2019