Blow up for the critical gKdV equation. II: Minimal mass dynamics

  • Yvan Martel

    École Polytechnique, Palaiseau, France
  • Frank Merle

    Université de Cergy-Pontoise, France
  • Pierre Raphaël

    Université de Nice Sophia Antipolis, France

Abstract

We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].

Cite this article

Yvan Martel, Frank Merle, Pierre Raphaël, Blow up for the critical gKdV equation. II: Minimal mass dynamics. J. Eur. Math. Soc. 17 (2015), no. 8, pp. 1855–1925

DOI 10.4171/JEMS/547