Well-posedness and large deviations for 2D stochastic constrained Navier-Stokes equations driven by Lévy noise in the Marcus canonical form

2021 ◽  
Vol 302 ◽  
pp. 64-138
Author(s):  
Utpal Manna ◽  
Akash Ashirbad Panda
Keyword(s):  
Large Deviations ◽  
Canonical Form ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Levy Noise

Stochastic Navier–Stokes equations perturbed by Lévy noise with hereditary viscosity

2019 ◽  
Vol 22 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Manil T. Mohan ◽  
Sivaguru S. Sritharan
Keyword(s):  
Stokes Equations ◽  
Past History ◽  
Local Solvability ◽  
Monotonicity Property ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Levy Noise

In this paper, we study the stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise in three dimensions with a hereditary viscous term which depends on the past history. We establish the local solvability of the Cauchy problem for such systems. The local monotonicity property of the nonlinear term of the cutoff problem and a stochastic generalization of the Minty–Browder technique are exploited in the proofs. Finally, we show that the global solvability results hold under smallness condition on the initial data and suitable assumptions on the noise coefficients.

STATIONARY WEAK SOLUTIONS FOR STOCHASTIC 3D NAVIER–STOKES EQUATIONS WITH LÉVY NOISE

2012 ◽  
Vol 12 (01) ◽  
pp. 1150006 ◽  
Author(s):  
ZHAO DONG ◽  
WENBO V. LI ◽  
JIANLIANG ZHAI
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Probability Measures ◽  
Stationary Probability ◽  
Navier Stokes Equations ◽  
Wiener Processes ◽  
The One ◽  
Levy Noise

We first study the existence of stationary weak solutions of stochastic 3D Navier–Stokes equations involving jumps, and the associated Galerkin stationary probability measures for this case. Then we present a comparison between the Galerkin stationary probability measures for the case driven by Lévy noise and the one driven by Wiener processes.

scholarly journals Ergodicity for the 3D stochastic Navier-Stokes equations perturbed by Lévy noise

2018 ◽  
Vol 292 (5) ◽  
pp. 1056-1088 ◽  
Author(s):  
Manil T. Mohan ◽  
K. Sakthivel ◽  
Sivaguru S. Sritharan
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Navier Stokes Equations ◽  
Levy Noise
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