Related papers: Gap Eigenvalues and Asymptotic Dynamics of Geometr…
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is the hyperbolic plane we proved in [13] the existence and…
In this paper we initiate the study of equivariant wave maps from 2d hyperbolic space into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than its Euclidean counterpart due to the exponential volume…
We study time and space equivariant wave maps from $M\times\RR\rightarrow S^2,$ where $M$ is diffeomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metric on $M$ can be written as…
We consider the Cauchy problem for the Schr\"odinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the Euclidean plane is the existence of a rich…
In this paper, we prove that the large energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation.
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\alpha$. Static solutions in this model are…
This is the first part of a two-paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the two-sphere valued equivariant energy critical wave maps…
We consider corotational wave maps from Minkowski spacetime into the sphere and the equivariant Yang-Mills equation for all energy-supercritical dimensions. Both models have explicit self-similar finite time blowup solutions, which continue…
The results of this paper are twofold: In the first part, we prove that for Schr\"odinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or…
This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general…
We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of $\beta$-damped stationary solutions cannot be completely…
In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation in the subcritical perturbation class. This result may be seen as an example supporting the…
We consider finite energy equivariant solutions for the wave map problem from R2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension two class of initial data which is small with respect to…
Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In…
In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally…
We consider the energy-critical wave maps equation $\mathbb R^{1+2} \to \mathbb S^2$ in the equivariant case, with equivariance degree $k \geq 2$. It is known that initial data of energy $ < 8k\pi$ and topological degree zero leads to…
We consider equivariant wave maps from the $(d+1)$--dimensional Minkowski spacetime into the $d$-sphere for $d\geq 4$. We find a new explicit stable self-similar solution and give numerical evidence that it plays the role of a universal…
This paper is concerned with the asymptotic stability of planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic-elliptic coupled system of the radiating gas in half space. We show that the solution…
We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi…
In this paper we use formal asymptotic arguments to understand the stability proper- ties of equivariant solutions to the Landau-Lifshitz-Gilbert model for ferromagnets. We also analyze both the harmonic map heatflow and Schrodinger map…