Related papers: Navier-Stokes and equivalence conjectures

A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called $L_{3,\infty}$-case.

We consider the wellposedness of the fractional Navier-Stokes as a generalization of the wellposedness result in Koch-Tataru's paper. An interesting remark is that our result does not contradict to the well-known ill-posedness result for…

This is largely an attempt to provide probabilists some orientation to an important class of non-linear partial differential equations in applied mathematics, the incompressible Navier-Stokes equations. Particular focus is given to the…

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…

Exploring the possibility of describing a fluid flow via a time-reversible equation and its relevance for the fluctuations statistics in stationary turbulent (or laminar) incompressible Navier-Stokes flows.

This paper considers the supercritical Navier-Stokes equations posed in the whole space $\R^d$, with suitably randomized initial data, in the weak solution setting. The global weak solutions are constructed for a large set of initial data…

Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes…

The goal of the paper is to understand properties of the so-called ancient (backward) solutions to the Navier-Stokes equations. We focus on the case of the half space.

There is renewed interest in the question of whether the Navier-Stokes equations (NSE), one of the fundamental models of classical physics and widely used in engineering applications, are actually self-consistent. After recalling the…

We explain why the theory of Escauriaza, Seregin, and Sverak (Russian Math. Surveys, 2003) on potential finite time singularity in Navier-Stokes solutions must be largely misapprehended. It is found that the proofs of the backward…

An Eulerian-Lagrangian approach to incompressible fluids that is convenient for both analysis and physics is presented. Bounds on burning rates in combustion and heat transfer in convection are discussed, as well as results concerning…

We review principal results on axiomatizability of classes of lattices of equivalences

We extend Barker's weak-strong uniqueness results for the Navier--Stokes equations and consider a criterion involving Besov spaces and weighted Lebesgue spaces.

New cases of the multiplicity conjecture are considered.

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…

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

We study bounded ancient solutions of the Navier-Stokes equations. These are the solutions which are defined for all past time. In two space dimensions we prove that such solutions are either constant or functions of time only, depending on…

We review some basic results on existence and uniqueness of the invariant measure for the two-dimensional stochastic Navier-Stokes equations. A large part of the literature concerns the additive noise case; after revising these models, we…

In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].