Related papers: A Liouville Type Theorem for Steady-State Navier-S…
We establish a new Liouville-type theorem for the stationary Navier--Stokes equations in $\mathbb{R}^3$. The main result is an improvement of the previous result with a logarithmic factor based on an understanding of $L^p$ growth of the…
Liouville type of theorems play a key role in the blow-up approach to study the global regularity of the three-dimensional Navier-Stokes equations. In this paper, we will prove Liouville type of theorems to the 3-D axisymmetric…
In this paper we study Liouville properties of smooth steady axially symmetric solutions of the Navier-Stokes equations. First, we provide another version of the Liouville theorem of \cite{kpr15} in the case of zero swirl, where we replaced…
In this manuscript, a new Liouville-type theorem for the three-dimensional stationary inhomogeneous Navier-Stokes equations is established. We first localize the Dirichlet energy into the region near the origin in frequency spaces by two…
We establish a Liouville theorem for bounded mild ancient solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb{T}^1)$. This is a step forward to completely solve the…
We prove Liouville type of theorems for weak solutions of the Navier-Stokes and the Euler equations. In particular, if the pressure satisfies $ p\in L^1 (0,T; L^1 (\Bbb R^N))$ with $\int_{\Bbb R^N} p(x,t)dx \geq 0$, then the corresponding…
In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in $\Bbb R^N$. If we assume "single signedness condition" on the force, then we can show that a $C^1 (\Bbb R^N)$…
Uniqueness of the trivial solution (the zero solution) for the steady-state Navier-Stokes equations is an interesting problem who has known several recent contributions. These results are also known as the Liouville type problem for the…
We prove some Liouville theorems for the stationary Navier-Stokes system for incompressible fluids. We provide some sufficient conditions on the low frequency part of the solution, using some properties of classical singular integrals with…
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
In this paper we prove Liouville type result for the stationary solutions to the compressible Navier-Stokes-Poisson equations(NSP) and the compressible Navier-Stokes equations(NS) in $\Bbb R^N$, $N\geq 2$. Assuming suitable integrability…
In this paper we prove a Liouville type theorem for generalized stationary Navier-Stokes systems in $\Bbb R^3$, which model non-Newtonian fluids, where the Laplacian term $\Delta u$ is replaced by the corresponding non linear operator…
Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations and under some additional hypotheses, stated in terms of…
Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…
We prove two Liouville type theorems for the stationary Navier-Stokes equations in $\mathbb{R}^3$ under some assumptions on 1) the growth of the $L^s$ mean oscillation of a potential function of the velocity field, or 2) the relative decay…
We study the stationary Navier--Stokes equations in the region between two rotating concentric cylinders. We first prove that, under the small Reynolds number, if the fluid is axisymmetric and if its velocity is sufficiently small in the…
We extend the Liouville-type theorems of Gilbarg and Weinberger and of Koch, Nadirashvili, Seregin and Sver\'ak valid for the stationary variant of the classical Navier-Stokes equations in 2D to the degenerate power law fluid model.
In the paper \cite{KNSS:1}, the authors make the following conjecture: {\it any bounded ancient mild solution of the 3D axially symmetric Navier-Stokes equations is constant.} And it is proved in the case that the solution is swirl free.…
This paper is concerned with the Liouville type theorems for the 3D stationary incompressible Hall-MHD equations. We establish that under some sufficient conditions in local Morrey spaces, solutions of the stationary Hall-MHD equations are…
We prove that suitable weak solutions of the Navier-Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying a Type I decay condition. The main novelty is in the…