Related papers: Navier-Stokes and equivalence conjectures
The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including…
The existence of global regular axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder is proved. The main step in the proof is a proof of the Holder continuity of the swirl. This gives a possibility to prove…
In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of…
We study in this article the solutions of the Navier-Stokes equations, with initial data in the closure of the Schwartz class in BMO-1. For such intial data, we obtain the existence and uniqueness of a global solution, and an estimate on…
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…
The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fields depending on a parameter R (Reynolds number). It is…
We show existence and regularity result for the Navier Stokes system for small data in the space $\Phi(2)$, and we show relations with some classical results.
We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.
It is argued that, at least for the case of Navier-Stokes fluids, the so-called hyperbolic theories of dissipation are not viable.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.
We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time H\"older continuous…
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
Extending the work of Jia and Sverak on self-similar solutions of the Navier-Stokes equations, we show the existence of large, forward, discretely self-similar solutions.
We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of initial data allowing growth at spatial infinity. Our work is a continuation of the results by T.-P. Tsai, Z. Bradshaw, I. Kukavica…
The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has know several recent contributions. We prove here some Liouville type theorems for these equations provided the…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
In this paper, we proved a special case of the DDVV Conjecture.
We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…
This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…