A large deviation principle for fluids of third grade

ABSTRACT

This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.

KEYWORDS:

• Large deviation principle
• non-Newtonian fluid
• stochastic partial differential equation
• third grade fluid
• weak convergence approach

AMS SUBJECT CLASSIFICATIONS:

• 60F10
• 76A05
• 60H15
• 60H30
• 37L55

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of A. Almeida was supported by the Calouste Gulbenkian Foundation, through the Scholarship Program for students from the PALOP and Timor-Leste. The work of F. Cipriano is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications).