36 citations · 69 across the 28 of their papers we have counts for
28 papers
Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions
Xiangsheng Xu
We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitabl…
Existence theorem for a partially parabolic cross-diffusion system
Xiangsheng Xu
We study an initial boundary value problem for a cross-diffusion system in population dynamics. The mathematical challenge is due to the fact that the determinant of the coefficien…
Exponential Crystal Relaxation Model With P-Laplacian
Brock C. Price, Xiangsheng Xu
In this article we prove the global existence of weak solutions to an initial boundary value problem with an exponential and p-Laplacian nonlinearity. The equation is a continuum l…
Hölder continuity of weak solutions to an elliptic-parabolic system modeling biological transportation network
Xiangsheng Xu
In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The system is singular and involves cubic nonlinearity.…
Modulus of continuity of weak solutions to a class of singular elliptic equations
Xiangsheng Xu
In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coef…
Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media
Xiangsheng Xu
In this paper we study the existence and partial regularity of weak solutions to an elliptic-parabolic system that models the single-phase miscible displacement of one incompressib…
Axion-like Particle Searches at DarkQuest
Nikita Blinov, Elizabeth Kowalczyk, Margaret Wynne
Axion-like particles (ALPs) interacting with the Standard Model can be abundantly produced in proton beam fixed-target experiments. Looking for their displaced decays is therefore…
Existence Theorems for a Fourth-Order Exponential PDE Related to Crystal Surface Growth
Brock C. Price, Xiangsheng Xu
In this article we prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE. The equation we study was origin…
Blow-up time of strong solutions to a biological network formation model in high space dimensions
Xiangsheng Xu
We investigate the possible blow-up of strong solutions to a biological network formation model originally introduced by D. Cai and D. Hu \cite{HC}. The model is represented by an…
Strong solutions to a fourth order exponential PDE describing epitaxial growth
Brock C. Price, Xiangsheng Xu
In this paper we prove the global existence of a strong solution to the initial boundary value problem for the exponential partial differential equation $\partial_tu-Δe^{-Δu}+e^{-Δ…
Existence and incompressible limit of a tissue growth model with autophagy
Jian-Guo Liu, Xiangsheng Xu
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existe…
Partial regularity for an exponential PDE in crystal surface models
Xiangsheng Xu
We study the regularity properties of a weak solution to the boundary value problem for the equation in a bounded domain , where $ρ=e^{-\mbox{div…
Nonlinear diffusion in the Keller-Segel model of parabolic-parabolic type
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $u_t-Δu^m=-\mbox{div}(u^{q}\nabla v),\ v_t-Δv+v=u$. This problem is the so-called Keller-Segel model with n…
Global existence theorem for a model governing the motion of two cell populations
Brock C. Price, Xiangsheng Xu
This article is concerned with the existence of a weak solution to the initial boundary problem for a cross-diffusion system which arises in the study of two cell population growth…
Global existence of strong solutions to a groundwater flow problem
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $Δv= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathb…
Regularity results for a nonlinear elliptic-parabolic system with oscillating coefficients
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system $\mbox{div}(σ(u)\nablaφ)=0,\ \ u_t-Δu=σ(u)|\nablaφ|^2$. This problem is known as the thermistor problem whi…
Global existence of strong solutions to a biological network formulation model in dimensions
Xiangsheng Xu
In this paper we study the initial boundary value problem for the system\\ $-\mbox{div}\left[(I+\mathbf{m} \mathbf{m}^T)\nabla p\right]=s(x),\ \ \mathbf{m}_t-α^2Δ\mathbf{m}+|\mathb…
Mathematical validation of a continuum model for relaxation of interacting steps in crystal surfaces in space dimensions
Xiangsheng Xu
In this paper we study the boundary value problem for the equation $\mbox{div}\left(D(\nabla u)\nabla\left(\mbox{div}\left(|\nabla u|^{p-2}\nabla u+β\frac{\nabla u}{|\nabla u|}\rig…
Special solutions to a fourth-order nonlinear parabolic equation in non-divergence form
Xiangsheng Xu
In this paper we study a crystal surface model first proposed by H.~Al Hajj Shehadeh, R.V.~Kohn, and J.~Weare (2011 Physica D, 240,1771-1784). By seeking a solution of a particular…
Existence theorems for a crystal surface model involving the p-Laplace operator
Xiangsheng Xu
The manufacturing of crystal films lies at the heart of modern nanotechnology. How to accurately predict the motion of a crystal surface is of fundamental importance. Many continuu…
Logarithmic upper bounds for weak solutions to a class of parabolic equations
Xiangsheng Xu
It is well known that a weak solution to the initial boundary value problem for the uniformly parabolic equation $\partial_tφ-\mbox{div}(A\nabla φ) +ωφ= f $ in $Ω_T\equivΩ\time…
Partial regularity of weak solutions and life-span of smooth solutions to a biological network formulation model
Xiangsheng Xu
In this paper we first study partial regularity of weak solutions to the initial boundary value problem for the system $-\mbox{div}\left[(I+\mathbf{m}\otimes \mathbf{m})\nabla p\ri…
Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
Yuan Gao, Jian-Guo Liu, Xin Yang Lu +1
In this work we consider which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the pr…
Local and global existence of solutions to a fourth-order parabolic equation modeling kinetic roughening and coarsening in thin films
Xiangsheng Xu
In this paper we study both the Cauchy problem and the initial boundary value problem for the equation $\partial_tu+\mbox{div}\left(\nablaΔu-{\bf g}(\nabla u)\right)=0$. This equat…