Abstract
We consider the initial value problem of a system of 2D nonlinear Schrödinger equations with quadratic nonlinearities in homogeneous Sobolev spaces which are close to the scale invariant spaces. We show the global solution, which is not necessarily in $\mathbf{L}^{2}( \mathbb{R}^{2})$, satisfies uniform time decay of order $|t|^{-1}$ in $\mathbf{L}^{\infty }( \mathbb{R}^{2})$.
Citation
Chunhua Li. "On a system of quadratic nonlinear Schrödinger equations and scale invariant spaces in 2D." Differential Integral Equations 28 (3/4) 201 - 220, March/April 2015. https://doi.org/10.57262/die/1423055224
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