Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208139We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrödinger equations i\partial_t u=-\epsΔu+Δ^2 u+P((\partial_x^αu)_{\absα\ls 2}, (\partial_x^α\bar{u})_{\absα\ls 2}),\quad t\in \Real, x\in\Real^n, where $\eps\in\{-1,0,1\}$, $n\gs 2$ denotes the spatial dimension and $P(\cdot)$ is a polynomial excluding constant and linear terms.28 pagesAnalysis of PDEs35Q55;35G25;35A07Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spacestext