Ke, Xueli Yuan, Baoquan Xiao, Yaomin
Published in
Acta Mathematica Scientia

This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L2-norm, where to prove the result...

Gao, Junpei Cui, Haibo
Published in
Acta Mathematica Scientia

We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line ℝ+ ≔ (0, ∞). Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, ...

Dong, Boqing Wu, Jiahong Xu, Xiaojing Zhu, Ning
Published in
Calculus of Variations and Partial Differential Equations

The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near the hydrostatic equilibrium of the Boussinesq system helps gain insight into certain weather phenomena. The 2D Boussinesq system focused here is anisotropic and involves only horizontal dissipation and horizontal th...

Akil, Mohammad Badawi, Haidar Nicaise, Serge Wehbe, Ali
Published in
Zeitschrift für angewandte Mathematik und Physik

In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin–Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt–Batty, we prove the strong stability of our system. Finally, using a frequency domai...

Audiard, Corentin Rodrigues, L. Miguel

The present contribution contains a quite extensive theory for the stability analysis of plane periodic waves of general Schrödinger equations. On one hand, we put the one-dimensional theory, or in other words the stability theory for longitudinal perturbations, on a par with the one available for systems of Korteweg type, including results on co-p...

Le, Phuong
Published in
Nonlinear Differential Equations and Applications NoDEA

We prove some Liouville type theorems for stable and finite Morse index solutions of the nonlinear Schrödinger system -Δui+λiui=∑j=1kβij|ui|q-1ui|uj|q+1inRN,i=1,⋯,k,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...

Lisai, Stefania Wilkinson, Mark
Published in
Journal of Mathematical Fluid Mechanics

We consider a class of steady solutions of the semi-geostrophic equations on R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^3$$\end{document} and deriv...

Sayevand, K. Ghanbari, N. Masti, I.
Published in
Computational and Applied Mathematics

In the last decade, the analysis of time-space fractional Bloch–Torrey equation has been considered by different studies due to its applications in many fields. Since the analytical solution of this equation is difficult or impossible, numerical solutions can be helpful and sometimes are the only choice. Therefore, in this work, a numerical-based s...

Xing, Jie Zheng, Pan Xiang, Yuting Wang, Hui
Published in
Zeitschrift für angewandte Mathematik und Physik

This paper deals with a fully parabolic singular chemotaxis-(growth) system with indirect signal production or consumption ut=Δu-χ∇·uv∇v+f(u),(x,t)∈Ω×(0,∞),vt=Δv+h(v,w),(x,t)∈Ω×(0,∞),wt=Δw-w+u,(x,t)∈Ω×(0,∞),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepack...

Hakkaev, Sevdzhan Stanislavova, Milena Stefanov, Atanas
Published in
Journal of Nonlinear Science

We study the periodic cubic derivative nonlinear Schrödinger equation (DNLS) and the (focussing) quintic nonlinear Schrödinger equation (NLS). These are both L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\...