相关论文: $L_q$-estimates for stationary Stokes system with …

We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction…

We consider a generalized steady Stokes system with discontinuous coefficients in a nonsmooth domain when the inhomogeneous term belongs to a weighted $L^q$ space for $2<q<\infty$. We prove the global weighted $L^q$-estimates for the…

This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and $L^\infty$ estimates for the pressure as…

We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation coefficients and data in a bounded domain containing a finite number of subdomains with $C^{1,\rm{Dini}}$ boundaries. We prove that if $(u, p)$ is a…

We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directions. We prove that if $(u,p)$ is a weak solution of the…

Concerned with the Stokes systems with rapidly oscillating periodic coefficients, we mainly extend the recent works in \cite{SGZWS,G} to those in term of Lipschitz domains. The arguments employed here are quite different from theirs, and…

We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm $L_{s,q}$-estimates hold for the spatial second-order…

We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…

We develop a new real-variable method for weighted $L^p$ estimates. The method is applied to the study of weighted $W^{1, 2}$ estimates in Lipschitz domains for weak solutions of second-order elliptic systems in divergence form with bounded…

We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a smooth domain. Since tissues can be modeled as…

We prove the solvability in Sobolev spaces of the conormal derivative problem for the stationary Stokes system with irregular coefficients on bounded Reifenberg flat domains. The coefficients are assumed to be merely measurable in one…

We consider a perturbed Stokes system with critical divergence-free drift in a bounded Lipschitz domain in $R^2$, with sufficiently small Lipschitz constant L. It extends our previous work in $\Bbb R^n, n\ge 3$, to two-dimensional case. For…

We establish resolvent estimates in spaces of bounded solenoidal functions for the Stokes operator in a bounded domain $\Omega$ in $R^d$ under the assumptions that $\Omega$ is $C^1$ for $d\ge 3$ and Lipschitz for $d=2$. As a corollary, it…

We consider the existence and $L^q$ gradient estimates for perturbed Stokes systems with divergence-free critical drift in a bounded Lipschitz domain in $\mathbb{R}^n$, $n \ge 3$. The first two results assume the drift is either in $L^n$ or…

This paper is devoted to the maximal $L^1$ regularity and asymptotic behavior for solutions to the inhomogeneous incompressible Navier-Stokes equations under a scaling-invariant smallness assumption on the initial velocity. We obtain a new…

We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having $C^{1,\rm{Dini}}$ boundary. We prove that if $(u, p)$ is a weak solution of the system with zero Dirichlet boundary condition, then $(Du,p)$ is…

We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain…

In this paper, we consider the generalized stationary Stokes system with $p$-growth and Dini-$\operatorname{BMO}$ regular coefficients. The main purpose is to establish pointwise estimates for the shear rate and the associated pressure to…

We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $\Omega$ in $\mathbb{R}^d$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(\Omega;…

We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder…