On the global well-posedness of energy-critical Schr\"odinger equations in curved spaces

By A. Ionescu, Benoit Pausader, Gigliola Staffilani. 2010

91 citations recorded by the source corpus.

In this paper we present a method to study global regularity properties of solutions of large-data critical Schrodinger equations on certain noncompact Riemannian manifolds. We rely on concentration compactness arguments and a global Morawetz inequality adapted to the geometry of the manifold (in other words we adapt the method of Kenig-Merle to the variable coefficient case), and a good understanding of the corresponding Euclidean problem (in our case the main theorem of Colliander-Keel-Staffilani-Takaoka-Tao). As an application we prove global well-posedness and scattering in $H^1$ for the energy-critical defocusing initial-value problem (i\partial_t+\Delta_\g)u=u|u|^{4} on the hyperbolic space $H^3$.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9694a61d3ca2a2e81ce9ef9a0ff118a24101b799

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

  1. Xiaoyi Zhang
  2. Monica Visan
  3. Rowan Killip
  4. Nikolay Tzvetkov
  5. Zaher Hani
  6. Benoit Pausader
  7. Aynur Bulut
  8. B. Dodson

In Mathematical Physics

  1. Rowan Killip
  2. Xiaoyi Zhang
  3. Benoit Pausader
  4. B. Dodson
  5. Monica Visan
  6. Vedran Sohinger
  7. Terence Tao
  8. Aynur Bulut

Citations in the corpus