Related papers: Global regular solutions for the Navier-stokes sys…

We prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Besov spaces $B^{r}_{p,q}(\mathbb{R}^n)$, $r>n/2p$. When $p=2$ and $n\geq 3$, we…

We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations \begin{align} u_t+(-\Delta)^{\alpha}u+u\cdot \nabla u +\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= u_0. \nonumber \end{align} We show the analyticity of…

In this paper, we study the global regularity of strong solution to the Cauchy problem of 3D incompressible Navier-Stokes equations with large data and non-zero force. We prove that the strong solution exists globally for $\nabla u\in…

In this short note we address a problem raised in [21], concerning the uniqueness of solutions to Naiver Stokes equation with small initial data in $L^{3,\infty}(R^3)$, the Lorentz space. We prove uniqueness for such initial data.

Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…

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…

The Cauchy problem and spatially periodic problem of incompressible Navier-Stokes equation are considered. The existence and uniqueness of global solution for these two problem with infinite smooth initial data $u_0$, i.e.…

First of all, we get the global existence of classical and strong solutions of the full compressible Navier-Stokes equations in three space dimensions with initial data which is large and spherically or cylindrically symmetric. The…

Regularity properties of strong solutions are considered.

In this paper, we study the 3D axi-symmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the…

We prove that for initial data of the form \begin{equation}\nonumber u_0^\epsilon(x) = (v_0^h(x_\epsilon), \epsilon^{-1}v_0^n(x_\epsilon))^T,\quad x_\epsilon = (x_h, \epsilon x_n)^T, n \geq 4, \end{equation} the Cauchy problem of the…

The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D…

We prove the existence of small amplitude, time-quasi-periodic solutions (invariant tori) for the incompressible Navier-Stokes equation on the $d$-dimensional torus $\T^d$, with a small, quasi-periodic in time external force. We also show…

In the note, various scenarios of potential Type II blowups of suitable weak solutions to the Navier-Stokes equations are studied. It is shown, that under some assumptions, such type of blowups cannot happen. In this case, corresponding…

This paper addresses a question concerning the behaviour of a sequence of global solutions to the Navier-Stokes equations, with the corresponding sequence of smooth initial data being bounded in the (non-energy class) weak Lebesgue space…

This work investigates the Cauchy problem for the classical Chemotaxis-Navier-Stokes (CNS) system in $\mathbb{R}^2$. We establish the global existence and uniqueness of strong, classical, and arbitrarily smooth solutions under large initial…

In a recent article, J.-Y. Chemin, I. Gallagher and M. Paicu obtained a class of large initial data generating a global smooth solution to the three dimensional, incompressible Navier-Stokes equations. This data varies slowly in the…

We here aim at proving the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density is discontinuous and the initial velocity has critical regularity.…

In this paper we prove that if we take to be identically zero and assume that any initial value satisfies on for any and then the Navier-Stokes initial value problem (1) have a smooth global solution , with bounded energy.

Global-in-time smooth self-similar solutions to the 3D Navier-Stokes equations are constructed emanating from homogeneous of degree -1 arbitrary large initial data belonging only to the closure of the test functions in the space of…