Related papers: Gradient estimates for Stokes and Navier-Stokes sy…

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. We prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying the condition $\lvert 1 / p…

We investigate the problem of classification of solutions for the steady Navier-Stokes equations in any cone-like domains. In the form of separated variables, $$u(x,y)=\left( \begin{array}{c} \varphi_1(r)v_1(\theta) \varphi_2(r)v_2(\theta)…

We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme utilizing new stationary building blocks designed…

Maximal $L^p$-$L^q$ regularity is proved for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain $\Omega$, not necessarily simply connected. This extends…

This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic…

In this paper we address the large-scale regularity theory for the stationary Navier-Stokes equations in highly oscillating bumpy John domains. These domains are very rough, possibly with fractals or cusps, at the microscopic scale, but are…

We study solutions to stationary Navier Stokes system in two dimensional exterior domain. We prove that any such solution with finite Dirichlet integral converges at infinity uniformly. No additional condition (on symmetry or smallness) are…

We study the partial regularity problem of the incompressible Navier--Stokes equations. In this paper, we show that a reverse H\"older inequality of velocity gradient with increasing support holds under the condition that a scaled…

We consider the 3D incompressible hypodissipative Navier-Stokes equations, when the dissipation is given as a fractional Laplacian $(-\Delta )^s$ for $s\in (\frac34,1)$, and we provide a new bootstrapping scheme that makes it possible to…

We consider the incompressible Navier-Stokes equations in a moving domain whose boundary is prescribed by a function $\eta=\eta(t,y)$ (with $y\in\mathbb R^2$) of low regularity. This is motivated by problems from fluid-structure…

This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…

In this paper, we prove global existence of weak solutions for the stationary compressible Navier-Stokes equations with an anisotropic and nonlocal viscous term in a periodic domain. This gives an answer to an open problem important for…

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…

We consider the steady Navier-Stokes system with mixed boundary conditions, in subdomains of a holdall domain. We study, via the penalization method, its approximation properties. Error estimates, obtained using the extension operator,…

We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…

The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first establish the $L^q_t(L^p)$-maximal regularity estimate for…

In this manuscript, we aim to establish global existence of weak solutions with higher regularity to the compressible Navier-Stokes equations under no-slip boundary conditions. Though Lions\cite{L1} and Feireisl\cite{F1} have established…

We prove a weak stability result for the three-dimensional homogeneous incompressible Navier-Stokes system. More precisely, we investigate the following problem : if a sequence $(u_{0, n})_{n\in \N}$ of initial data, bounded in some scaling…

In this paper, we consider the inhomogeneous Dirichlet boundary value problem for the stationary Navier--Stokes equations in $n$-dimensional half spaces $\mathbb{R}^n_+= \{ x=(x',x_n)\ ;\ x' \in \mathbb{R}^{n-1}, x_n > 0 \}$ with $n \geq 3$…

In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial…