Bound · version 1
For Leray–Hopf weak solutions, ∫₀ᵀ ‖u(τ)‖_{L^q}^{4q/(3(q−2))} dτ ≤ C K₀^{2q/(3(q−2))} for 2 ≤ q ≤ 6, where K₀ is the initial kinetic energy.
These are the norms every weak solution controls. Each satisfies 2/p + 3/q = 3/2, above the regularity threshold 2/p + 3/q ≤ 1.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Kang–Protas · Ladyzhenskaya–Prodi–Serrin conditions · p. 3, estimate (12); derived in Appendix A →
Observed Oct 21, 2026
In this problem · publication v8
Supporting result · Proved
Relationship not independently reviewed. This concerns its use in this problem.
An a priori bound valid also for Leray–Hopf weak solutions: the time integral of the L^q norm to the power 4q/(3(q−2)) is bounded by the initial energy, for 2 ≤ q ≤ 6.
paraphrase · No upstream full text is republished by this record.
Di Kang · Bartosz Protas · Published · Publication date Sep 6, 2022
Published in Journal of Nonlinear Science 32, article 81 (2022), DOI 10.1007/s00332-022-09832-7. Statements here use the pinned arXiv v1: the abstract and estimate (12).
Source revision: arxiv-v1. Observed Oct 21, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Oct 11, 2021.
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Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026 · Source passage →