Related papers: Logarithmically Improved Criteria for Navier-Stoke…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
We extend the well-known Serrin's blowup criterion for the three-dimensional (3D) incompressible Navier-Stokes equations to the 3D viscous compressible cases. It is shown that for the Cauchy problem of the 3D compressible Navier-Stokes…
This paper presents an analytic solution of the incompressible Navier-Stokes equations as recurrence relations for the solution's derivatives, addressing the Clay Mathematics Institute's Millennium Prize problem on Navier-Stokes existence…
In Benzi & Olshanskii (SIAM J.~Sci.~Comput., 28(6) (2006)) a preconditioner of augmented Lagrangian type was presented for the two-dimensional stationary incompressible Navier--Stokes equations that exhibits convergence almost independent…
A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the propose scheme. Convergence of the discrete velocity is…
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…
A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations…
We study the partial regularity of suitable weak solutions to the three dimensional incompressible Navier--Stokes equations. There have been several attempts to refine the Caffarelli--Kohn--Nirenberg criterion (1982). We present an improved…
For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…
We formulate a new criterion for regularity of a suitable weak solution v to the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of…
We study the Cauchy problem for the 3D Navier-Stokes equations, and prove some scalaring-invariant regularity criteria involving only one velocity component.
We prove some estimates for suitable weak solutions to the non-stationary three-dimensional Navier-Stokes equations under assumptions that certain invariant functionals of the velocity are bounded.
We give conditions for regularity of solutions of three dimensional incompressible Navier-Stokes equations based on the pressure and on structure functions.
In this paper we establish a Serrin type regularity criterion on the gradient of pressure in weak spaces for the Leray-Hopf weak solutions of the Navier-Stokes equations in R3.
A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called $L_{3,\infty}$-case.
In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in…
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…
The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L$^2$ norm in time and in space.…
In this paper, let $\mathcal{S}$ denote the possible interior singular set of suitable weak solutions of the 3D Navier-Stokes equations. We improve the known upper box-counting dimension of this set from $360/277(\approx1.300)$ in [24] to…