Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

We consider the Schrödinger map initial-value problem \cases∂_tϕ=ϕ*Δϕ\,on\BbbR^d*\
BbbR,&\ϕ(0)=ϕ_0,&\endcases where ϕ: ℝ d× ℝ→ 𝕊 2↪ ℝ 3 is a smooth function. In all …

We consider the wave maps equation with values into a Riemannian manifold which is
isometrically embedded in [inline-graphic xmlns: xlink=" http://www. w3. org/1999/xlink" xlink …

In this article we consider large data Wave-Maps from\mathbb R^ 2+ 1 into a compact
Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as …

Wave maps are the simplest wave equations taking their values in a Riemannian manifold
$(M, g) $. Their Lagrangian is the same as for the scalar equation, the only difference being …

The Cauchy Problem for Wave Maps Page 1 IMRN International Mathematics Research
Notices 2002, No. 11 The Cauchy Problem for Wave Maps Jalal Shatah and Michael Struwe …

The wave maps equation has become a very popular topic in recent years. The aim of these
expository notes is to present a non-technical survey of the ideas and methods which have …

We study the question of well-posedness of the Cauchy problem for Schrödinger maps from
ℝ× ℝ 2 to the sphere 2 or to ℍ 2, the hyperbolic space. The idea is to choose an …

Abstract We demonstrate that Wave Maps with smooth initial data and small energy from R
2+ 1 to the Lobatchevsky plane stay smooth globally in time. Our method is similar to the one …

We show that wave maps $\phi $ from two-dimensional Minkowski space $\R^{1+ 2} $ to
hyperbolic spaces $\H^ m $ are globally smooth in time if the initial data is smooth …