TY - JOUR
T1 - Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in Lp^-spaces
AU - Hyakuna, Ryosuke
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
KW - Cauchy problem
KW - Hartree equation
KW - Local well-posedness
KW - Nonlinear Schrödinger equations
UR - http://www.scopus.com/inward/record.url?scp=85042628436&partnerID=8YFLogxK
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U2 - 10.1007/s00028-018-0432-8
DO - 10.1007/s00028-018-0432-8
M3 - Article
AN - SCOPUS:85042628436
SN - 1424-3199
SP - 1
EP - 16
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
ER -