相关论文: Liouville theorem for Beltrami flow

In this paper, we study the Liouville-type property for smooth solutions to the steady 3D tropical climate model. We prove that if a smooth solution $(u,v,\theta)$ satisfies $u \in L^3 (\mathbb{R}^3)$, $v \in L^2 (\mathbb{R}^3)$, and…

Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with…

The fluid ball conjecture states that a static perfect fluid space-time is spherically symmetric. In this paper we construct a Robinson's divergence formula for the static perfect fluid space-time. Inspired by this conjecture, a rigidity…

Generalizations of the Jacobi and Weyl theorems on finite-dimensional linear flows to the case of linear flows on infinite-dimensional tori are presented. Conditions for periodicity, non-wandering, ergodicity and transitivity of…

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…

In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(\rho, \mathbf{u})$ satisfies suitable conditions.

We establish Liouville type theorems for elliptic systems with various classes of non-linearities on $\mathbb{R}^N$. We show among other things, that a system has no semi-stable solution in any dimension, whenever the infimum of the…

We establish a Liouville type theorem for some conformally invariant fully nonlinear equations

We prove Liouville theorem for the equation $\Delta_m v + v^p + M |\nabla v|^{q}= 0$ in a domain $\Omega\subset\mathbb R^n$, with $M\in \mathbb{R}$ in the critical and subcritical case. As a natural extension of our recent work \cite{MWZ},…

We construct a new finite difference method for the flow of ideal viscous isentropic gas in one spatial dimension. For the continuity equation, the method is a standard upwind discretization. For the momentum equation, the method is an…

Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus $\mathbb T^3$. The building blocks in their proof are Beltrami flows, which are inherently…

We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity…

In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group ${\mathbb Z}_2 \times {\mathbb Z}_3$ (in fact, he offers two proofs of this result). In this note we give a…

The aim of this article is to provide a Liouville theorem for heat equation along ancient super Ricci flow. We formulate such a Liouville theorem under a growth condition concerning Perelman's reduced distance.

We characterise the boundary field line behaviour of Beltrami flows on compact, connected manifolds with vanishing first de Rham cohomology group. Namely we show that except for an at most nowhere dense subset of the boundary, on which the…

Given $\Bbb R^2, $ with a ``good'' complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on…

We prove that the correspondence between Reeb and Beltrami vector fields can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that…

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of…

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 consider the incompressible 3D Euler and Navier-Stokes equations in a smooth bounded domain. First, we study the 3D Euler equations endowed with slip boundary conditions and we prove the same criteria for energy…