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 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.
Citation
Soichiro Katayama. Chunhua Li. Hideaki Sunagawa. "A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D." Differential Integral Equations 27 (3/4) 301 - 312, March/April 2014. https://doi.org/10.57262/die/1391091368
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