Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity
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 nonlin...
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AFIT Scholar
2019
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| Mynediad Ar-lein: | https://scholar.afit.edu/facpub/459 |
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| _version_ | 1870453234291703808 |
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| author | Mohan, Manil T. Sritharan, Sivaguru S. |
| author_facet | Mohan, Manil T. Sritharan, Sivaguru S. |
| author_sort | Mohan, Manil T. |
| building | US Air Force Institute of Technology (AFIT) |
| collection | AFIT Scholar |
| description | 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. |
| format | text |
| id | afit-facpub-1468 |
| institution | US Air Force Institute of Technology |
| publishDate | 2019 |
| publisher | AFIT Scholar |
| record_format | dspace |
| spelling | afit-facpub-1468 Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity Mohan, Manil T. Sritharan, Sivaguru S. 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. 2019-04-08T07:00:00Z text https://scholar.afit.edu/facpub/459 info:doi/<a href="https://doi.org/10.1142/S0219025719500061">10.1142/S0219025719500061</a> Faculty Publications AFIT Scholar Stochastic Navier–Stokes equations Lévy noise Hereditary viscosity Non-Newtonian fluids Monotonicity Local and global strong solution 35Q30 Partial Differential Equations |
| spellingShingle | Stochastic Navier–Stokes equations Lévy noise Hereditary viscosity Non-Newtonian fluids Monotonicity Local and global strong solution 35Q30 Partial Differential Equations Mohan, Manil T. Sritharan, Sivaguru S. Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title | Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title_full | Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title_fullStr | Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title_full_unstemmed | Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title_short | Stochastic Navier–Stokes Equations Perturbed by Lévy Noise with Hereditary Viscosity |
| title_sort | stochastic navier stokes equations perturbed by levy noise with hereditary viscosity |
| topic | Stochastic Navier–Stokes equations Lévy noise Hereditary viscosity Non-Newtonian fluids Monotonicity Local and global strong solution 35Q30 Partial Differential Equations |
| url | https://scholar.afit.edu/facpub/459 |
| work_keys_str_mv | AT mohanmanilt stochasticnavierstokesequationsperturbedbylevynoisewithhereditaryviscosity AT sritharansivagurus stochasticnavierstokesequationsperturbedbylevynoisewithhereditaryviscosity |