Related papers: Global weak solutions of the Navier-Stokes equatio…

We construct global smooth solutions to the incompressible Navier--Stokes equations in $\mathbb{R}^3$ for initial data in $L^2$ satisfying some smallness condition. The high-frequency part is assumed to be small in $BMO^{-1}$, while the…

We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…

We give a condition for the periodic, three dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the…

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations \begin{equation*} \partial_t u + u \cdot \nabla u = \Delta u - \nabla p + \zeta + \xi \;, \quad u (0, \cdot) = u_{0}(\cdot) \;, \quad…

We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but possibly large oscillations where the initial…

We prove space-time decay estimates of suitable weak solutions to the Navier-Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result…

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an…

We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.

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…

In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces , using Calder{\'o}n splitting L p $\Phi$$\gamma$ $\subset$ L 2 $\Phi$ 2 + L r (with some r $\in$ (3, +$\infty$))…

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…

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…

This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk…

In 1934 Leray proved that the Navier-Stokes equations have global weak solutions for initial data in $L^2(\mathbb{R}^N)$. In 1990 Calder\'on extended this result to the initial value spaces $L^p(\mathbb{R}^N)$ ($2\leq p<\infty$). In the…

In this paper, we study the initial-boundary value problem of the Navier-Stokes equations in half-space. Let a solenoidal initial velocity be given in the function space $ \dot{B}_{p\infty,0}^{ -1 + n/p}({\mathbb R}^n_+)$ for $ \frac{n}3< p…

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 $L_3(\mathbb R^3)$

We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…