On blowup solutions to the focusing intercritical nonlinear fourth-order Schrödinger equation

2018/01/25 by Dinh, Van Duong
#35B44 #35G20 #35G25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08866

Abstract

In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schrödinger equation. We firstly establish the profile decomposition of bounded sequences in H^γ_c ∩ H². We also prove a compactness lemma and a variational characterization of ground states related to the equation. As a result, we obtain the H^γ_c-concentration of blowup solutions with bounded H^γ_c-norm and the limiting profile of blowup solutions with critical H^γ_c-norm.

Related

• Dynamics of radial solutions for the focusing fourth-order nonlinear\n Schr "odinger equations
• Blow-up for the nonlinear Schrödinger equation with combined nonlinearities
• Global existence and blowup for a class of the focusing nonlinear\n Schr "odinger equation with inverse-square potential
• On blowup solutions to the focusing L²-supercritical nonlinear fractional Schrödinger equation
• On the blowup for the L²-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class