Finite-time divergence of kinetic-energy fluctuations in a Schrödinger-induction flow
Abstract
In this study, we use a constrained Schrödinger--induction system to investigate kinetic-energy fluctuations induced by a fluid singularity. Assuming the cited Navier--Stokes construction with zero initial velocity and its exact exterior profile, we construct a periodic trajectory from a constant normalized wave function and zero connection. The prescribed body force admits a smooth space--time extension across the normalized singular time t=1. In this construction, the probability density remains constant and the mean matter kinetic energy stays bounded, whereas the gauge-invariant kinetic-energy variance diverges. We prove a lower growth bound of order (1−t)−1/2−5h, with h fixed by the source construction, by integrating the fourth power of the complete velocity's magnitude over an exact exterior region where all oscillatory corrections vanish. After fixing a gauge with constant wave function, we identify a unique weak L2 connection limit outside L4 and construct its positive self-adjoint kinetic operator through the associated magnetic form. We further show that the normalized endpoint state belongs to the form domain but not the operator domain: its first kinetic spectral moment is finite, whereas its second is infinite. These results connect fluid concentration to a loss of kinetic-domain regularity and provide a dynamical benchmark for assessing the limits of mean-energy control in hydrodynamic wave formulations.
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BibTeX
@misc{liu2026finitetime,
title = {{Finite-time divergence of kinetic-energy fluctuations in a Schrödinger-induction flow}},
author = {Weishuo Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10085},
eprint = {2609.10085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10085},
}
RIS
TY - UNPB
TI - Finite-time divergence of kinetic-energy fluctuations in a Schrödinger-induction flow
AU - Weishuo Liu
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10085
UR - https://arxiv.org/abs/2609.10085
AB - In this study, we use a constrained Schrödinger--induction system to investigate kinetic-energy fluctuations induced by a fluid singularity. Assuming the cited Navier--Stokes construction with zero initial velocity and its exact exterior profile, we construct a periodic trajectory from a constant normalized wave function and zero connection. The prescribed body force admits a smooth space--time extension across the normalized singular time t=1. In this construction, the probability density remains constant and the mean matter kinetic energy stays bounded, whereas the gauge-invariant kinetic-energy variance diverges. We prove a lower growth bound of order (1−t)^−1/2−5h, with h fixed by the source construction, by integrating the fourth power of the complete velocity's magnitude over an exact exterior region where all oscillatory corrections vanish. After fixing a gauge with constant wave function, we identify a unique weak L^2 connection limit outside L^4 and construct its positive self-adjoint kinetic operator through the associated magnetic form. We further show that the normalized endpoint state belongs to the form domain but not the operator domain: its first kinetic spectral moment is finite, whereas its second is infinite. These results connect fluid concentration to a loss of kinetic-domain regularity and provide a dynamical benchmark for assessing the limits of mean-energy control in hydrodynamic wave formulations.
ER -