Related papers: On the Energy Equality for Distributional Solution…

It is well-known that a Leray-Hopf weak solution in $L^4 (0,T; L^4(\Omega))$ for the incompressible Navier-Stokes system is persistence of energy due to Lions [19]. In this paper, it is shown that Lions's condition for energy balance is…

When a Leray--Hopf weak solution to the NSE has a singularity set $S$ of dimension $d$ less than $3$---for example, a suitable weak solution---we find a family of new $L^q L^p$ conditions that guarantee validity of the energy equality. Our…

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and $\n u$ belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy…

It is well known that a Leray-Hopf weak solution enjoys an energy inequality. Here, we investigate the energy equality related to a suitable weak solution to the Navier-Stokes initial boundary value problem. The term suitable is meant in…

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 present note we establish the following inequality for the the Leray-Hopf solutions of the 3-D $\Omega$-periodic Navier-Stokes Equations: \[\phi(|u(t)|^2)-\phi(|u(t_0)|^2)\le 2\int_{t_0}^{t}\phi'(|u(\tau)|^2)…

We prove that the energy equality holds for weak solutions of the 3D Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where $V^{5/6}$ is the domain of the fractional power of the Stokes operator $A^{5/12}$.

We provide a sharp result that guarantees that a distributional solution satisfying the Prodi-Serrin condition is regular in the spatial variables. The solution does not need to belong to the (local) Leray-Hopf class.

We show non-uniqueness of local strong solutions to stochastic fractional Navier-Stokes equations with linear multiplicative noise and some certain deterministic force. Such non-uniqueness holds true even if we perturb such deterministic…

We show that the classical Shinbrot's criteria to guarantee that a Leray-Hopf solution satisfies the energy equality follows trivially from the $L^4( (0\,,T)\times\Omega))$ Lions-Prodi particular case. Moreover we extend Shinbrot's result…

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}…

Under the assumption of an initial datum divergence free and in L2, we prove the existence of a weak solution to the Navier-Stokes initial boundary value problem enjoying the energy equality on (0,t), almost everywhere in t>0, in…

Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energy equality for weak solutions in a large class of function…

We study the three-dimensional Navier-Stokes equations forced by space-time white noise and diffused via the fractional Laplacian with Lions' exponent so that it is precisely the energy-critical case. We prove its global solution theory…

In this paper we study the problem of energy conservation for the solutions of the initial boundary value problem associated to the 3D Navier-Stokes equations, with Dirichlet boundary conditions. First, we consider Leray-Hopf weak solutions…

In this paper, we provide a sufficient condition of the energy equality for the incompressible Navier-Stokes equations in bounded domains.

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…

Recently, strong evidence has accumulated that some solutions to the Navier-Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is to establish necessary properties for the error of…

We show that a Leray-Hopf weak solution to the 3D Navier-Stokes Cauchy problem belonging to the space $L^\infty(0,T; B^{-1}_{\infty,\infty}(\mathbb R^3))$ is regular in $(0,T]$. As a consequence, it follows that any Leray-Hopf weak solution…

In this paper, we are concerned with the minimal regularity of both the density and the velocity for the weak solutions keeping energy equality in the isentropic compressible Navier-Stokes equations. The energy equality criteria without…