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 Korea
  • JinMyong Kim

    Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea
  • PyongJo Ryu

    Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea
Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces cover
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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