Related papers: On the regularity set and angular integrability fo…

We propose a data assimilation algorithm for the 2D Navier-Stokes equations, based on the Azouani, Olson, and Titi (AOT) algorithm, but applied to the 2D Navier-Stokes-Voigt equations. Adapting the AOT algorithm to regularized versions of…

Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on…

Using the concept of stationary statistical solution, which generalizes the notion of invariant measure, it is proved that, in a suitable sense, time averages of almost every Leray-Hopf weak solution of the three-dimensional incompressible…

We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to $H^{1/2}$ almost surely, we establish the existence and uniqueness of a local-in-time probabilistically strong…

The aim of the note is to discuss different definitions of solutions to the Cauchy problem for the Navier-Stokes equations with the initial data belonging to the Lebesgue space $L_3(\mathbb R^3)$

By using defect measures, we prove the existence of partially regular weak solutions to the stationary Navier-Stokes equations with external force $f \in L_{\text{loc}}^q \cap L^{3/2}, q>3$ in general open subdomains of $\mathbb{R}^6$.…

We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…

This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…

We study the partial regularity problem of the three-dimensional incompressible Navier--Stokes equations. We present a new boundary regularity criterion for boundary suitable weak solutions. As an application, a bound for the parabolic…

In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in…

A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully…

In this paper, we consider the initial-boundary value problem to the nonhomogeneous incompressible Navier-Stokes equations. Local strong solutions are established, for any initial data $(\rho_0, u_0)\in (W^{1,\gamma} \cap L^\infty)\times…

We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…

Regularity and uniqueness of weak solutions of the compressible barotropic Navier-Stokes equations with constant viscosity coefficients is proven for small time in dimension $N=2,3$ under periodic boundary conditions. In this paper, the…

In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…

We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…

A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at least one global weak solution which can be obtained as the…

We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the…

This article is devoted to a regularity criteria for solutions of the Navier-Stokes equations in terms of regularity along the stream lines. More precisely, we prove that a suitable weak solution for the Navier-Stokes equations is regular…

We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if…