Related papers: Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces

In this paper we prove, if $u\in\mathcal C([0,\infty),{\bf {\mathcal X}^{-1}}(\mathbb R^3))$ is global solution of 3D Navier-Stokes equations, then $\|u(t)\|_{{\bf {\mathcal X}^{-1}}}$ decays to zero as time goes to infinity. Fourier…

In this paper we prove, if $u$ is a global solution to Navier-Stokes equations in the Sobolev-Gevrey spaces $H^1_{a,\sigma}(\mathbb R^3)$, then $\|u(t)\|_{H^1_{a,\sigma}}$ decays to zero as time goes to infinity. Fourier analysis is used.

In this paper, we prove that if $u\in C([0,\infty), \dot{H}^{1/2}_{a,1}(\mathbb{R}^3))$ is a global solution of 3D incompressible Navier-Stokes equations, then $\|u\|_{\dot{H}^{1/2}_{a,1}}$ decays to zero as time approaches infinity.…

In this paper we study the incompressible Navier-Stokes equations in $L^2(\mathbb R^3)\cap\mathcal X^{-1}(\mathbb R^3)$. In the global existence case, we establish that if the solution $u$ is in the space $C(\mathbb R^+,L^2\cap\mathcal…

In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $\alpha|u|^{\beta-1}u(\alpha>0,\;\beta\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the…

We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show…

We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).

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 obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of initial data allowing growth at spatial infinity. Our work is a continuation of the results by T.-P. Tsai, Z. Bradshaw, I. Kukavica…

We study regularity criteria for the $d$-dimensional incompressible Navier-Stokes equations. We prove in this paper that if $u\in L_\infty^tL_{d}^x((0,T)\times {\mathbb R}^d)$ is a Leray-Hopf weak solution, then $u$ is smooth and unique in…

In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…

We consider the 3-D Navier-Stokes initial value problem, $$ v_t - \nu \Delta v = -\mathcal{P} [ v \cdot \nabla v ] + f , v(x, 0) = v_0 (x), x \in \mathbb{T}^3 (*) $$ where $\mathcal{P}$ is the Hodge projection. We assume that the Fourier…

We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with the nonlinear exponential damping term $a (e^{b |u|^{\bf 2}}-1)u$, ($a,b>0$) studied…

In this work we consider the Navier-Stokes problem modified by the absorption term $|\textbf{u}|^{\sigma-2}\textbf{u}$, where $\sigma>1$, which is introduced in the momentum equation. % For this new problem, we prove the existence of weak…

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…

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are…

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D…

In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.

In this paper we prove the existence and uniqueness of strong solution of the incompressible Navier-Stokes equations with damping $\alpha (e^{\beta|u|^2}-1)u$.

In this paper, we prove the global existence, uniqueness and the continuity in $L^2$ of the incompressible Navier-Stokes equations with damping $f(|u|)u$, where $f$ is an increasing, convex and differentiable function on $\mathbb{R}^+$,…