相关论文: Stationary Solutions of the Curvature Preserving F…
We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions,…
In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate…
In this paper we analyze the motion of a network of three planar curves with a speed proportional to the curvature of the arcs, having perpendicular intersections with the outer boundary and a common intersection at a triple junction. As a…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
Given a compact four dimensional smooth Riemannian manifold $(M,g)$ with smooth boundary, we consider the evolution equation by $Q$-curvature in the interior keeping the $T$-curvature and the mean curvature to be zero and the evolution…
In this paper, we study curve shortening flows on rotational surfaces in $\mathbb{R}^3$. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of embedded curve…
Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of…
In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami type, that can…
Dufty, Lee, Lutsko, Montanero, and Santos have carried out stability analyses of steady stationary shear flows. Their approach is based on the compressible and heat conducting Navier-Stokes-Fourier model. It predicts the unstable…
We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic…
We show that the solutions to the curvature flow (CF) for curves on the 2-dimensional light cone are in correspondence with the solutions to the inverse curvature flow (ICF). We prove that the ellipses and the hyperboles are the only curves…
Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the…
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure…
This survey reviews some facts about nonnegativity conditions on the curvature tensor of a Riemannian manifold which are preserved by the action of the Ricci flow. The text focuses on two main points. First we describe the known examples of…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
We consider the flat flow solutions of the mean curvature equation with a forcing term in the plane. We prove that for every constant forcing term the stationary sets are given by a finite union of disks with equal radii and disjoint…
We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the m-th mean curvature plus a volume preserving term, including the case of powers of the mean curvature…
The flow of an ideal fluid possesses a remarkable property: despite limited regularity of the velocity field, its particle trajectories are analytic curves. In our previous work, this fact was used to introduce the structure of an analytic…
The aim of this paper is to study the $L^1$-stability of periodic stationary solutions of scalar convection-diffusion equations. We obtain dispersion in $L^2$ for all space dimensions using Kru\v{z}kov type entropy. And when the space…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…