Related papers: Backward Uniqueness for 3D Navier-Stokes Equations…
Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity is integrable with…
We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with…
In this paper, we investigate the global well-posedness for the 3-D inhomogeneous incompressible Navier-Stokes system with the axisymmetric initial data. We prove the global well-posedness provided that $$\|\frac{a_{0}}{r}\|_{\infty}…
We prove the existence of strong solutions to Navier-Stokes equations in three dimensional thin domains. Our proof is based on the energy and the Poincar\'e inequalities as well as contraction principle argument and is free of the mean…
In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
We prove existence of global-in-time weak solutions of the incompressible Navier-Stokes equations in the half-space $\mathbb{R}^3_+$ with initial data in a weighted space that allow non-uniformly locally square integrable functions that…
We study the Navier-Stokes equations in dimension 3 (NS3D) driven by a noise which is white in time. We establish that if the noise is at same time sufficiently smooth and non degenerate in space, then the weak solutions converge…
In this paper we rule out the possibility of asymptotically self-similar singularities for both of the 3D Euler and the 3D Navier-Stokes equations. The notion means that the local in time classical solutions of the equations develop…
Some known results regarding the Euler and Navier-Stokes equations were obtained by different authors. Existence and smoothness of solutions for the Navier-Stokes equations in two dimensions have been known for a long time. Leray showed…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
We construct self-similar solutions to the 2D Navier--Stokes equations evolving from arbitrarily large $-1$--homogeneous initial data and present numerical evidence for their non-uniqueness.
It is shown both locally and globally that $L_t^{\infty}(L_x^{3,q})$ solutions to the three-dimensional Navier-Stokes equations are regular provided $q\not=\infty$. Here $L_x^{3,q}$, $0<q\leq\infty$, is an increasing scale of Lorentz spaces…
We show the existence of (a class of) weak solutions to the three-dimensional stationary incompressible inhomogeneous Navier--Stokes equations with density-dependent viscosity coefficient in the axially symmetric case. Further symmetric…
We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely…
In this paper, it is shown that there does not exist a non-trivial Leray's backward self-similar solution to the 3D Navier-Stokes equations with profiles in Morrey spaces $\dot{\mathcal{M}}^{q,1}(\mathbb{R}^{3})$ provided $3/2<q<6$, or in…
The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
We consider the initial value problem for the Navier-Stokes equations over $R^{3} \times [0,T]$ with a positive time $T$ in the spatially periodic setting. Identifying periodic vector-valued functions on $R^{3}$ with functions on the…