Related papers: Space-time decay of Navier-Stokes flows invariant …
Around forty years ago, Michael Wiegner provided, in a seminal paper, sharp algebraic decay rates for solutions of the Navier--Stokes equations, showing that these solutions behave asymptotically like the solutions of the heat equation with…
In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to some subspace of $\mathrm{BMO}^{-1}$, and the initial density is sufficiently…
This paper is devoted to the global (in time) regularity problem for a family of active scalar equations with fractional dissipation. Each component of the velocity field $u$ is determined by the active scalar $\theta$ through $\mathcal{R}…
We prove in this paper a decay estimate for scaling invariant local energy solutions for some toy-models related to the incompressible Navier-Stokes system.
In this paper, we show existence and non-uniqueness on the axially symmetric stationary Navier-Stokes equations in an exterior periodic cylinder. On the boundary of the cylinder, the horizontally swirl velocity is subject to the…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density…
By applying Wiegner' method in \cite{Wiegner}, we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
This work is concerned with the large time behavior of solutions to the barotropic compressible Navier-Stokes equations in $\mathbb{R}^{d}(d\geq2)$. Precisely, it is shown that if the initial density and velocity additionally belong to some…
Let w be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane -\infty<x<\infty, y>1, with zero Dirichlet boundary conditions at y=1 and at…
We use the general exact solution of the Cauchy problem for the compressible Euler vortex equation in unbounded space which was obtained earlier (S.G.Chefranov, Sov. Phys. Dokl., 36, 286, 1991). This solution loses its smoothness in finite…
We consider the 2D incompressible Navier-Stokes equations on $\mathbb{T}\times \mathbf{R}$, with initial vorticity that is $\delta$ close in $H^{log}_xL^2_{y}$ to $-1$(the vorticity of the Couette flow $(y,0)$). We prove that if $\delta\ll…
This work explores Navier-Stokes equation with no gravitational forces. In short, it shows that any smooth solution that decays quickly must take the form $$ \textbf{u}(x,t)- \dfrac{1}{4\pi}\textbf{Curl}\Biggl(…
We introduce and analyze a space-time least-squares method associated to the unsteady Navier-Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess,…
In this paper we consider smooth solutions of the Navier--Stokes equations with a linear dependence on the spatial variable. We reduce the evolution of these solutions to a matrix ODE, and show that there are such solutions that blowup in…
The periodic $3D$ Navier-Stokes equations are analyzed in terms of dimensionless, scaled, $L^{2m}$-norms of vorticity $D_{m}$ ($1 \leq m < \infty$). The first in this hierarchy, $D_{1}$, is the global enstrophy. Three regimes naturally…
In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants,…
We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in…
Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows where they often emerge on time-scales much shorter than the viscous time scale, and then dominate the dynamics for very long time…