Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces
JinMyong An
Kim Il Sung University, Pyongyang, Democratic People’s Republic of KoreaJinMyong Kim
Kim Il Sung University, Pyongyang, Democratic People's Republic of KoreaPyongJo Ryu
Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea
Abstract
In this paper, we study the Cauchy problem for the inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation
where , , , and . Under some regularity assumption for the nonlinear term, we prove that the IBNLS equation is locally well-posed in if , , and . Here if , and if . Our local well-posedness result improves the ones of Guzmán–Pastor (2020) and Liu–Zhang (2021) by extending the validity of and .
Cite this article
JinMyong An, JinMyong Kim, PyongJo Ryu, Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces. Z. Anal. Anwend. 41 (2022), no. 1/2, pp. 239–258
DOI 10.4171/ZAA/1707