On the dynamics of a quadratic Schrödinger system in dimension n=5

2018/10/02 by Noguera, Norman, Pastor, Ademir · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.01390

Abstract

In this work we give a sharp criterion for the global well-posedness, in the energy space, for a system of nonlinear Schrödinger equations with quadratic interaction in dimension n=5. The criterion is given in terms of the charge and energy of the ground states associated with the system, which are obtained by minimizing a Weinstein-type functional. The main result is then obtained in view of a sharp Gagliardo-Nirenberg-type inequality.

Cited by

• Energy critical fourth-order Schrödinger equation system with power-type nonlinearities in the radial case
• The focusing energy-critical nonlinear Schrödinger system with power-type growth nonlinearities in the radial case

Related

• Global dynamics below the ground state for the quadratic Schödinger system in 5d
• Threshold solutions for the energy-critical NLS system with quadratic interaction
• Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
• Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six
• On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation