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Unconditional well-posedness for the nonlinear Schrodinger equation in Bessel potential spaces

Year: 2025

Type: article

Abstract: The Cauchy problem for the nonlinear Schrodinger equation is called unconditionally well posed in a data space \(E\) if it is well posed in the usual sense and the solution is unique in the space \(C([0,T]; E)\). In this paper, this notion of the unconditional well-posedness is redefined so that it covers \(L^p\)-based Sobolev spaces as data space \(E\) and it is equivalent to the usual one when \(E\) is an \(L^2\)-based Sobolev space \(H^s\) Based on this definition, it is shown that the Cauchy problem for the 1D cubic NLS is unconditionally well posed in Bessel potential spaces \(H^s_p\) for \(4/3

Source: Electronic Journal of Differential Equations

DOI: 10.58997/ejde.2025.41

Author: Ryosuke Hyakuna

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: LP theory for the nonlinear Schrodinger and dispersive equations

OpenAlex ID: W4409557663

FWCI: 1.7

Cites:

Cited by: 1

Related to: 10