Pith. sign in

REVIEW 2 cited by

Nonuniqueness of weak solutions of the nonlinear Schroedinger equation

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0503366 v1 pith:SYL7SJVE submitted 2005-03-17 math.AP

Michael Christ This is my paper · ORCID
classification math.AP
keywords solutionsequationgeneralizednonlinearcauchycertaincontinuouslydata
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schr\"odinger equation, with certain nonlinearities, are not unique. For any $s<0$ there exist nonzero generalized solutions varying continuously in the Sobolev space $H^s$, with identically vanishing initial data.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Intermittent singular solutions of the stationary 2D Navier-Stokes equations in sharp Sobolev spaces

    math.AP 2025-06 conditional novelty 7.0 of 10

    Nontrivial stationary solutions of the 2D Navier-Stokes equations exist on the torus at regularity L^{2-epsilon} cap dot H^{-epsilon} for every epsilon in (0,1).

  2. Non-unique solutions to the periodic gKdV equation

    math.AP 2026-06 unverdicted novelty 6.0 of 10

    Non-unique weak solutions to periodic k-gKdV are constructed via convex integration in low-regularity spaces with zero initial data, establishing that nonlinearity integrability is necessary for unconditional uniqueness.

Pith tools