Related papers: Smooth Solutions of the Navier-Stokes Equation in …

We prove the global existence and uniqueness of smooth solutions to the one-dimensional barotropic Navier-Stokes system with degenerate viscosity $\mu(\rho)=\rho^\alpha$. We establish that the smooth solutions have possibly two different…

This paper discussed the existence and uniqueness of the smoothing solution of the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant…

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…

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…

We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the $N$-dimensional Euclidean space for $N\geq 2$ when the gravity is not taken into account. The aim of this paper is…

In this paper, we establish the global existence and uniqueness of solution to $2$-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.2} with initial data in the critical spaces. Precisely, under the assumption that the initial…

This article examines the smoothness of the solution to the Navier-Stokes equation from a novel perspective. Here, the existence of the smoother solution relative to x and to the time t was shown only for a finite time. Moreover, for each…

It is well known that the Navier-Stokes equations have unique global strong solutions for standard domains when initial data are small in $L^n_\sigma$. Global well-posedness has been extended to rough initial data in larger critical spaces.…

This paper studies an initial boundary value problem for the multidimensional hyperbolized compressible Navier-Stokes equations, in which the classical Newtonian law is replaced by the Maxwell law. We seek spherically symmetric solutions to…

We consider the Cauchy problem to the axisymmetric Navier-Stokes equations. To prove an existence of global regular solutions we examine the Navier-Stokes equations near the axis of symmetry and far from it separately. We derive only a…

In this paper, we consider the model of 3D incompressible Navier-Stokes equations and 2D supercritical Surface Quasi-Geostrophic equations with time oscillation in the nonlinear term. We obtain that there exists global smooth solution of…

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…

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and $\n u$ belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy…

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…

It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations…

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…

The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…

We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…

Using clean numerical simulation (CNS) which can give very accurate spatiotemporal trajectory of Navier-Stokes turbulence in a finite but long enough interval of time, we give some numerical evidences that the Navier-Stokes equations admit…

A domain in $\mathbb{R}^3$ that touches the $x_3$ axis at one point is found with the following property. For any initial value in a $C^2$ class, the axially symmetric Navier Stokes equations with Navier slip boundary condition has a finite…