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A Class of Stochastic Partial Differential Equations with Jumps in Fluid Dynamics: Large and Moderate Deviation Asymptotics

  • Arnab Ganguly
  • Padmanabhan Sundar
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Abstract

We establish large and moderate deviation principles for a broad class of nonlinear stochastic partial differential equations driven by multiplicative Poisson random measures in the small-noise regime. Our abstract framework is formulated for locally monotone evolution equations over a Hilbert triple and encompasses several important models arising in fluid dynamics and turbulence theory, including the two-dimensional Navier--Stokes equations, magnetohydrodynamics (MHD), the GOY shell model of turbulence, the two-dimensional tidal equations, and Navier--Stokes equations with nonlinear viscosities. A key analytical ingredient is the well-posedness of the associated controlled equations, established using the method of local monotonicity. The large and moderate deviation principles are then proved via the weak convergence approach.

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Cite

BibTeXRIS
BibTeX
@misc{ganguly2026class,
  title = {{A Class of Stochastic Partial Differential Equations with Jumps in Fluid Dynamics: Large and Moderate Deviation Asymptotics}},
  author = {Arnab Ganguly and Padmanabhan Sundar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05837},
  eprint = {2610.05837},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05837},
}
RIS
TY  - UNPB
TI  - A Class of Stochastic Partial Differential Equations with Jumps in Fluid Dynamics: Large and Moderate Deviation Asymptotics
AU  - Arnab Ganguly
AU  - Padmanabhan Sundar
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05837
UR  - https://arxiv.org/abs/2610.05837
AB  - We establish large and moderate deviation principles for a broad class of nonlinear stochastic partial differential equations driven by multiplicative Poisson random measures in the small-noise regime. Our abstract framework is formulated for locally monotone evolution equations over a Hilbert triple and encompasses several important models arising in fluid dynamics and turbulence theory, including the two-dimensional Navier--Stokes equations, magnetohydrodynamics (MHD), the GOY shell model of turbulence, the two-dimensional tidal equations, and Navier--Stokes equations with nonlinear viscosities. A key analytical ingredient is the well-posedness of the associated controlled equations, established using the method of local monotonicity. The large and moderate deviation principles are then proved via the weak convergence approach.
ER  -