A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D

Abstract

We consider the initial value problem for a three-component system of quadratic nonlinear Schrödinger equations with mass resonance in two space dimensions. Under a suitable condition on the coefficients of the nonlinearity, we will show that the solution decays strictly faster than $O(t^{-1})$ as $t\to +\infty$ in $L^{\infty }$ by providing with an enhanced decay estimate of order $O((t\log t{)}^{-1})$. Differently from the previous works, our approach does not rely on the explicit form of the asymptotic profile of the solution at all.

12 pages

Cited by in corpus (4)

• Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
• Null structure in a system of quadratic derivative nonlinear Schrödinger equations
• Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities
• Semilinear hyperbolic systems violating the null condition