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

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 \(s\). For more information see https://ejde.math.txstate.edu/Volumes/2025/41/abstr.html