Related papers: Critical one component anisotropic regularity for …

This paper is concerned with the localized behaviors of the solution $u$ to the Navier-Stokes equations near the potential singular points. We establish the concentration rate for the $L^{p,\infty}$ norm of $u$ with $3\leq p\leq\infty$.…

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…

We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly…

In this article, we develop a new method, based on a time decomposition of a Cauchy problem elaborated in [6], to retrieve the well-known $L^\infty ([0,T],L^2(\mathbb{R}^d,\mathbb{R}^d))$ control of the solution of the incompressible…

In this paper, we consider a model equation for the Navier--Stokes strain equation. This model equation has the same identity for enstrophy growth and a number of the same regularity criteria as the full Navier-Stokes strain equation, and…

A mathematical evidence -- in a statistically significant sense -- of a geometric scenario leading to criticality of the Navier-Stokes problem is presented.

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…

We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to the 3-D compressible Navier-Stokes equations. The initial vacuum is allowed. The main ingredient of the proof is \textit{a priori} estimate…

We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time…

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…

For any divergence free initial datum $u_0$ with $\|u_0\|_\infty+\|\nabla u_0\|_{L^p}+\|\nabla^2 u_0\|_{L^p}<\infty$ for some $p>d\ (d\ge 2)$, the well-posedness and smoothness are proved for incompressible Navier-Stokes equations on…

Classical vorticity solution branches of the three dimensional incompressible Euler equation are constructed where a velocity component can blow up at some point after finite time for regular data in H2. Furthermore, vorticity can blow up…

For a perturbed trefoil vortex knot evolving under the Navier-Stokes equations, a sequence of $\nu$-independent times $t_m$ are identified corresponding to a set of scaled, volume-integrated vorticity moments $\nu^{1/4}{\it O}_{V1}$ with…

We investigate the three-dimensional incompressible Navier-Stokes equations. The equations are discretized with Fourier spectral method and a fourth-order Runge-Kutta scheme in time. The spectral accuracy, resolution conditions, and an…

The purpose of this paper is to study the vanishing viscosity limit for the d-dimensional Navier--Stokes equations in the whole space: \begin{equation*} \begin{cases} \partial_tu^\varepsilon+u^\varepsilon\cdot \nabla…

Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…

The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain $\mathcal{D}\subset\mathbb{R}^d$ for $d\leq3$. Under appropriate conditions on the initial data, the nonlinear…

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow.…

Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity is integrable with…

It is shown both locally and globally that $L_t^{\infty}(L_x^{3,q})$ solutions to the three-dimensional Navier-Stokes equations are regular provided $q\not=\infty$. Here $L_x^{3,q}$, $0<q\leq\infty$, is an increasing scale of Lorentz spaces…