Global Existence for Wave Maps with Torsion

Local and Global Well-posedness of Wave Maps on R for Rough Data

We consider wave maps between Minkowski space R and an analytic manifold. Results include global existence for large data in Sobolev spaces Hs for s > 3/4, and in the scale-invariant norm L1,1. We prove local well-posedness in Hs for s > 3/4, and a negative well-posedness result for wave maps on R with data in Hn/2(R), n ≥ 1. Also included are positive and negative results for scattering.

Torsion Effect on the RC Structures using Fragility Curves Concerning Soil-Structure Interaction

The existence of torsion, as well as consideration of the Soil-Structure Interaction (SSI), increase the natural periods of the structure resulting from a subsequent decrease in the seismic demand of the system. This paper summarizes the probabilistic assessment for evaluation of collapse fragility curves in concrete moment resisting structure with different mass center eccentricities. A 12-sto...

The University of Chicago on the Global Behavior of Wave Maps a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Mathematics by Andrew

We study wave maps equation in three distinct settings. First, we prove a small data result for wave maps on a curved background. To be specific, we consider the Cauchy problem for wave maps u : R×M → N , for Riemannian manifolds (M, g) and (N, h). We prove global existence and uniqueness for initial data, (u0, u1), that is small in the critical norm Ḣ d 2 × Ḣ d2−1(M ;TN), in the case (M, g) = ...

Global Existence of Wave Maps in 1 + 2 Dimensions with Finite Energy Data

An Algebraic Characterization for the Characteristic Tensors of an Infinitesimally Homogeneous Manifold

Given a Lie subgroup H ⊂ GL(R) and H-invariant multilinear maps on R of type curvature, torsion and inner torsion, we give necessary and sufficient conditions for the existence of an infinitesimally homogeneous affine manifold with H-structure whose characteristic tensors are those given.