NLS References

From PDEwiki

NLS Blowup Lecture Series Plan

• Merle, F.; Raphaël, P., Sharp upper bound on the blowup rate for critical nonlinear Schrödinger equation, Geom. Funct. Analysis 13 (2003), 591-642

• Merle, F.; Raphaël, P., On Universality of Blowup Profile for L² critical nonlinear Schrödinger equation, Invent. Math. 156 (2004), 565-672

Energy Critical Lecture Series Plan

• Energy Critical Wave Equations
  • Radial Case
  • Nonradial case
  • Does induction on energy strategy provide a simpler proof?

• Energy Critical Defocusing Schrodinger Equations
  • Radial Case (Tao:NYJM)
  • Nonradial case in (CKSTT:Annals)
  • Nonradial case in (Visan-Ryckman)
  • General dimensions (Visan) (Tao-Visan)
  • Energy critical case in

• Energy Critical Focusing Schrodinger Equations
  • Radial result, d=3,4,5. (Kenig-Merle)
  • Replacing localized Morawetz by localized virial for radial case (Tao:NYJM) (Tao:Note on Kenig-Merle)
  • Other dimensions?
  • nonradial?

• Mass Critical Case

• -critical case, 0 < s_c < 1.

• -critical case, s_c > 1 (Energy Supercritical)? (Tao:LogSuper)