Related papers: Rooted trees for 3d Navier-Stokes equation
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…
This paper is concerned with the global solvability for the Navier-Stokes equations describing viscous free surface flows of infinite depth in three and higher dimensions. We first prove time weighted estimates of solutions to a linearized…
In this paper, we study local regularity of the solutions to the Stokes equations near a curved boundary under no-slip or Navier boundary conditions. We extend previous boundary estimates near a flat boundary to that near a curved boundary,…
In this paper, we investigate the three dimensional stationary compressible Navier-Stokes equations, and obtain Liouville type theorems if a smooth solution $(\rho, \mathbf{u})$ satisfies some suitable conditions. In particular, our results…
In this paper, we study the singular set of 3-dimensional Navier-Stokes equations. Under the condition$\frac{1}{R^{\frac{3s}{q}+2-s}}\int^{R^{2}}_{0}(\int_{B_{R}}|u|^{q}dx)^{\frac{s}{q}}ds <C,$ for $(q,s)\in\{(2,5),(5,2)\},$ we use the…
The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has been proven for initial data in the Sobolev space…
An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal,…
We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are H\"older continuous up to the boundary provided that the…
We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove…
We prove that suitable weak solutions of the Navier-Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying a Type I decay condition. The main novelty is in the…
We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…
We obtain a new inequality that holds for general Leray solutions of the incompressible Navier-Stokes equations in Rn (n <= 4). This recovers important results previously obtained by other authors regarding the time decay of solution…
In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4}…
We investigate the problem of classification of solutions for the steady Navier-Stokes equations in any cone-like domains. In the form of separated variables, $$u(x,y)=\left( \begin{array}{c} \varphi_1(r)v_1(\theta) \varphi_2(r)v_2(\theta)…
Forward self-similar and discretely self-similar weak solutions of the Navier-Stokes equations are known to exist globally in time for large self-similar and discretely self-similar initial data and are known to be regular outside of a…
We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…
We prove the unique existence of solutions of the 3D incompressible Navier-Stokes equations in an exterior domain with small non-decaying boundary data, for $t \in R$ or $t \in (0,\infty)$. In the latter case it is coupled with small…
We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme utilizing new stationary building blocks designed…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…