A moderate deviation principle for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises. (English) Zbl 1356.60100
The authors consider an incompressible Navier-Stokes equation \(u_t-\nu\Delta u+(u\cdot\nabla)u+\nabla p=f\) with homogeneous Dirichlet boundary condition on a bounded domain \(D\) in \(\mathbb R^2\). This equation is perturbed in a multiplicative way by a compensated Poisson random measure on a locally compact Polish space with the intensity measure \(\varepsilon^{-1}\lambda\otimes\vartheta\). If \(u\) denotes the solution of the unperturbed (deterministic) equation and \(u^\varepsilon\) is the solution of the perturbed (stochastic) equation for \(\varepsilon>0\), then a large deviation principle for \((u^\varepsilon-u)/a(\varepsilon)\) with speed \(\varepsilon a^{-2}(\varepsilon)\) is proved. Here, \(a\) is assumed to satisfy \(a(\varepsilon)\to 0\) and \(\varepsilon a^{-2}(\varepsilon)\to 0\) as \(\varepsilon\to 0\).
Reviewer: Martin Ondreját (Praha)
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60F10 | Large deviations |
| 60G51 | Processes with independent increments; Lévy processes |
| 60G57 | Random measures |
| 35Q30 | Navier-Stokes equations |
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