Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 41, pp. 1-8.

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

Author: Ryosuke Hyakuna (Polytechnic Univ. of Japan, Tokyo, Japan)

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 $4/3<p\le 2$ under certain assumptions on $s$.

Submitted August 24, 2024. Published April 16, 2025.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger equation; unconditional well-posedness; L^p-space;
 Bessel potential space.