Polytechnic University of Japan
Tokyo, Japan
email: 107r107r@gmail.com
Ryosuke Hyakuna
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 15, 2025.
Math Subject Classifications: 35Q55.
Key Words: Nonlinear Schrodinger equation; unconditional well-posedness; L^p-space;
Bessel potential space.
DOI: 10.58997/ejde.2025.41
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Ryosuke Hyakuna Polytechnic University of Japan Tokyo, Japan email: 107r107r@gmail.com |
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