Related papers: On Liouiville Type Theorem for the 3D Isentropic N…
In this article we study some Liouville-type theorems for the stationary 3D Navier-Stokes equations. These results are related to the uniqueness of weak solutions for this system under some additional information over the velocity field,…
We establish various results concerning the uniqueness of zero velocity solutions for the static barotropic Navier--Stokes system. Some of them can be seen as Liouville-type theorems for problems in unbounded physical space.
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…
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.…
We study axially symmetric $D$-solutions of three dimensional steady Navier-Stokes equations. We prove that if the velocity $u$ decays like $|x'|^{-(\frac{2}{3})^+}$ uniformly for $z$, or the vorticity $\omega$ decays like…
We consider entire solutions $u$ of the equations describing the stationary flow of a generalized Newtonian fluid in 2D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of $u$ implies its…
We show that any smooth solution $(\mathbf{u},\mathbf{H})$ to the stationary equations of magneto-hydrodynamics (MHD) belonging to both spaces $L^6 (\mathbb{R}^3)$ and $BMO^{-1}(\mathbb{R}^3)$ must be identically zero. This is an extension…
In \cite{CV23}, Chamorro and Vergara-Hermosilla established several Liouville-type theorems to the Navier-Stokes equations in the framework of the variable Lebesgue spaces. These results may allow the variable exponent $p(\cdot)$ beyond the…
In this paper we study the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$. We deduce an asymptotic formula for an integral involving the head pressure, $Q=\frac12 |v|^2 +p$, and its derivative over domains…
In this paper, we investigate the Liouville-type theorems for axisymmetric solutions to steady Navier-Stokes system in a layer domain. The both cases for the flows supplemented with no-slip boundary and Navier boundary conditions are…
In this paper, we investigate the steady simplified Ericksen-Leslie system. For three dimension, we obtain Liouville theorems if $u$ and $\nabla d$ satisfy the Galdi's[1] condition, or some decay conditions. Note that the simplified…
We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related…
In this paper, we generalize the main results of [1] and [31] to Lorentz spaces, using a simple procedure. The main results are the following. Let $n\geq 3$ and let $u$ be a Leray-Hopf solution to the $n$-dimensional Navier-Stokes equations…
We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assumptions on the antiderivative of the velocity that represent…
We investigate existence, Liouville type theorems and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power…
In this paper we prove some Liouville-type theorems for the stationary magneto-micropolar fluids under suitable conditions in three space dimensions. We first prove that the solutions are trivial under the assumption of certain growth…
We study the asymptotic behavior of axisymmetric solutions with no swirl to the steady Navier-Stokes equations in the outside of the cylinder. We prove an a priori decay estimate of the vorticity under the assumption that the velocity has…
In this paper, we derive several new sufficient conditions of non-breakdown of strong solutions for for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations. First, it is…
We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed.…
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…