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, ...

Gao, Jincheng Huang, Daiwen Yao, Zheng-an
Published in
Calculus of Variations and Partial Differential Equations

In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics (MHD) equations, which are derived from the two-dimensional density-dependent incompressible MHD equations. Under the assumption that initial tangential magnetic field is not zero and density is a small perturbation of the...

Yang, Hui Wang, Changjia
Published in
Mediterranean Journal of Mathematics

In this paper, we consider a steady MHD fluid model of non-Newtonian type in a smooth bounded domain Ω∈R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \in {\ma...

Xu, Xiangsheng
Published in
SN Partial Differential Equations and Applications

In this paper we study partial regularity of weak solutions to the initial boundary value problem for the system -div(I+m⊗m)∇p=S(x),∂tm-D2Δm-E2(m·∇p)∇p+|m|2(γ-1)m=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setleng...

Xu, Xiangsheng
Published in
Zeitschrift für angewandte Mathematik und Physik

In this paper, we study the initial boundary value problem for the system Δv=ux1,ut-div(a|q|+m)I+(b-a)q⊗q|q|∇u=-∇u·q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Del...

Dreyer, Wolfgang Druet, Pierre-Étienne Gajewski, Paul Guhlke, Clemens
Published in
Zeitschrift für angewandte Mathematik und Physik

We consider an improved Nernst–Planck–Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non-equilibrium. The elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, is taken into account. The model consists of convection–diffusion–reaction equations for the...

Zhou, Shuang-shuang Gong, Ting Yang, Jin-ge
Published in
Applied Mathematics-A Journal of Chinese Universities

We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion Chemotaxis systems {ut=∇⋅(ϕ(u)∇u)+∇⋅(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...

Li, Bin
Published in
Results in Mathematics

This paper deals with a parabolic-elliptic-parabolic system arising from ion transport networks originally proposed by Albi et al. (Anal Appl 14(1):185–206, 2016). Our investigation demonstrates that the local existence of the weak solution can always be achieved. Moreover, by establishing the uniform a-priori decay estimates of solution, the local...

Hou, Meichen
Published in
Acta Mathematica Scientia

This article is concerned with the impermeable wall problem for an ideal poly-tropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof is given by an elementary energy method and the key point is to do the higher order derivative e...

Xie, Feng Yang, Tong
Published in
Acta Mathematicae Applicatae Sinica, English Series

In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in [12], the lifespan of solution is shown to have a lower bound in the order of ε−2− if the strength of the perturbation is of the order of ε. Since there...