Dynamics of Partial Differential Equations
Volume 7 (2010)
Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation
Pages: 187 – 205
This paper is concerned with the blow-up solutions of the focusing fourth-order mass-critical nonlinear Schrödinger equation. Establishing the profile decomposition of the bounded sequences in H², we obtain the variational characteristics of the corresponding ground state and a compactness lemma. Moreover, we obtain the L²-concentration of the blow-up solutions and the limiting profile of the minimal mass blow-up solutions in the general case.
nonlinear Schrödinger equation, Blow-up solution, Profile decomposition, Limiting profile
2010 Mathematics Subject Classification