Zhihong Chen, Dongsheng Li. Source: Advances in Differential Equations, Volume 26, Number 1/2, 83--106.Abstract: In this paper, we consider a system related to Maxwell's equations, which has different structure with general elliptic systems. The existence of the weak solution is obtained in...

Yanan Li, Zhijian Yang. Source: Advances in Differential Equations, Volume 26, Number 1/2, 45--82.Abstract: The paper investigates the existence of strong global and exponential attractors and their continuity for a class of semilinear wave equations with fractional damping in $\Omega\subset...

Xiaoming Wang, Hao Wu. Source: Advances in Differential Equations, Volume 26, Number 1/2, 1--44.Abstract: We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three...

Gary M. Lieberman. Source: Advances in Differential Equations, Volume 25, Number 11/12, 709--754.Abstract: We prove a gradient bound for solutions of a large class of oblique derivative problems using the maximum principle. Although many of the results in this work are already known, the advantage...

Sitong Chen, Xianhua Tang. Source: Advances in Differential Equations, Volume 25, Number 11/12, 687--708.Abstract: This paper is concerned with the following planar Schrödinger-Poisson system with zero mass \begin{equation*} \begin{cases} -\Delta u+\lambda \phi u=f(x,u), \;\; & x\in {\mathbb...

Martin Saal. Source: Advances in Differential Equations, Volume 25, Number 11/12, 651--685.Abstract: We consider the $3D$ primitive equations and show, that one does need less than horizontal viscosity to obtain a well-posedness result in Sobolev spaces. Furthermore, we will also investigate the...

Matania Ben-Artzi, Michael Ruzhansky, Mitsuru Sugimoto. Source: Advances in Differential Equations, Volume 25, Number 11/12, 627--650.Abstract: Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the...

Tatsu-Hiko Miura. Source: Advances in Differential Equations, Volume 25, Number 9/10, 457--626.Abstract: We consider the Navier–Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions, we show that...

Sihua Liang, Nguyen Thanh Chung, Binlin Zhang. Source: Advances in Differential Equations, Volume 25, Number 7/8, 423--456.Abstract: In this article, we consider the existence of multi-bump solutions for a class of the fractional Schrödinger equation with external magnetic field and critical...

Xiaopeng Zhao. Source: Advances in Differential Equations, Volume 25, Number 7/8, 373--422.Abstract: In this paper, by using the properties of decay character and the Fourier splitting method, we establish the time decay rates of solutions for three-dimensional incompressible electron inertial...