Stochastic Tamed Navier--Stokes Equations with Wiener and Jump Noise on ℝ3. II. Global Lp Well-Posedness
Abstract
We establish intrinsic continuation criteria and finite-energy global solvability for the stochastic tamed Navier--Stokes equations on ℝ3 driven simultaneously by multiplicative cylindrical Wiener and compensated Poisson noise. Under local coefficient hypotheses, the maximal local Lp solution, p>3, satisfies a blow-up alternative independent of auxiliary cutoffs and a Serrin criterion with time exponent 2p/(p−3). Additional coercivity of the taming term and compatible L2 and gradient noise bounds yield the global well-posedness theory for divergence-free initial data u0∈ Lp(Ω;Lp)∩ L2(Ω;L2). No smallness or initial H1 regularity is required. The solution has càdlàg Lp∩ L2 paths and gains H1 regularity at positive times, with time-weighted H1 and H2 estimates. The proof combines finite-energy persistence with endpoint completion that retains terminal Poisson jumps and permits restart in the original uniqueness class.
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BibTeX
@misc{podder2026stochastic,
title = {{Stochastic Tamed Navier--Stokes Equations with Wiener and Jump Noise on $\mathbb R^3$. II. Global $L^p$ Well-Posedness}},
author = {Bikram Podder and Surendra Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29411},
eprint = {2609.29411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29411},
}
RIS
TY - UNPB
TI - Stochastic Tamed Navier--Stokes Equations with Wiener and Jump Noise on ℝ^3. II. Global L^p Well-Posedness
AU - Bikram Podder
AU - Surendra Kumar
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29411
UR - https://arxiv.org/abs/2609.29411
AB - We establish intrinsic continuation criteria and finite-energy global solvability for the stochastic tamed Navier--Stokes equations on ℝ^3 driven simultaneously by multiplicative cylindrical Wiener and compensated Poisson noise. Under local coefficient hypotheses, the maximal local L^p solution, p>3, satisfies a blow-up alternative independent of auxiliary cutoffs and a Serrin criterion with time exponent 2p/(p−3). Additional coercivity of the taming term and compatible L^2 and gradient noise bounds yield the global well-posedness theory for divergence-free initial data u_0∈ L^p(Ω;L^p)∩ L^2(Ω;L^2). No smallness or initial H^1 regularity is required. The solution has càdlàg L^p∩ L^2 paths and gains H^1 regularity at positive times, with time-weighted H^1 and H^2 estimates. The proof combines finite-energy persistence with endpoint completion that retains terminal Poisson jumps and permits restart in the original uniqueness class.
ER -