Semi-martingale driven variational principles

Abstract

Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational principle and constraining the component variables to be compatible with the driving semi-martingale. Within this framework and the corresponding choice of constraints, the Euler-Poincare equation can be easily deduced. We show that their corresponding deterministic counterparts are particular cases of this class of stochastic variational principles. Moreover, this is a natural framework that enables us to correctly characterize the pressure term in incompressible stochastic fluid models. Other general constraints can also be incorporated as long as they are compatible with the driving semi-martingale.

arXiv comment25 pages

References in corpus (13)

• Variational Principles for Stochastic Fluid Dynamics
• Fluid flow dynamics under location uncertainty
• Solution properties of a 3D stochastic Euler fluid equation
• Stochastic Variational Integrators
• Geophysical flows under location uncertainty, Part II: Quasi-geostrophy and efficient ensemble spreading
• Geophysical flows under location uncertainty, Part I Random transport and general models
• Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
• Wave breaking for the Stochastic Camassa-Holm equation
• Stochastic Discrete Hamiltonian Variational Integrators
• Variational Principles for Stochastic Soliton Dynamics
• Implications of Kunita-Itô-Wentzell formula for $k$-forms in stochastic fluid dynamics
• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• Stochastic Parametrization of the Richardson Triple

Cited by in corpus (11)

• Stochastic mesoscale circulation dynamics in the thermal ocean
• Stochastic effects of waves on currents in the ocean mixed layer
• Data-driven stochastic Lie transport modelling of the 2D Euler equations
• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• Qubit fidelity under stochastic Schrödinger equations driven by colored noise
• Fidelity-Enhanced Variational Quantum Optimal Control
• Variational Stochastic Parameterisations and their Applications to Primitive Equation Models
• Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
• On Stochastic Variational Principles
• Fidelity Relations in an Array of Neutral Atom Qubits -- Experimental Validation of Control Noise
• A stochastic Hamiltonian formulation applied to dissipative particle dynamics