This paper is concerned with the Cauchy problem of the Schrödinger equation with polynomial-type nonlinearities and the Hartree equation. It is shown that these Cauchy problems are locally well posed in (Formula presented.) under certain conditions on p, where (Formula presented.)Local solutions are constructed in a function space based on the fundamental theorem of calculus and the free Schrödinger group (Formula presented.), which was originally used by YI.Zhou.
ASJC Scopus subject areas
- Mathematics (miscellaneous)