Shell model of turbulence perturbed by Lévy noise

de Acosta A.: A general non-convex large deviation result with applications to stochastic equations. Prob. Theory Relat. Fields 118, 483–521 (2000)

de Acosta A.: Large deviations for vector valued Lévy processes. Stoch. Process. Appl. 51, 75–115 (1994)

Albeverio S., Wu J.L., Zhang T.S.: Parabolic SPDEs driven by Poisson white noise. Stoch. Process. Appl. 74, 21–36 (1998)

Applebaum, D.: Lévy Processes and Stochastic Calculus. In: Cambridge Studies in Advanced Mathematics, vol. 93. Cambridge University press, Cambridge (2004)

Barbato D., Barsanti M., Bessaih H., Flandoli F.: Some rigorous results on a stochastic Goy model. J. Stat. Phys. 125(3), 677–716 (2006)

Bensoussan A., Temam R.: Equations aux dérivées partielles stochastiques non linéaries(1). Isr. J. Math. 11(1), 95–129 (1972)

Brzeźniak Z., Hausenblas E.: Maximal regularity for stochastic convolutions driven by Lévy processes. Probab. Theory Relat. Fields 145, 615–637 (2009)

Constantin P., Levant B., Titi E.S.: Analytic study of shell models of turbulence. Phys. D 219(2), 120–141 (2006)

Fournier N.: Malliavin calculus for parabolic SPDEs with jumps. Stoch. Process. Appl. 87(1), 115–147 (2000)

Hausenblas E.: Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure. Electron. J. Probab. 10, 1496–1546 (2005)

Ikeda N., Watanabe S.: Stochastic differential equations and diffusion processes. North-Holland/Kodansha, Amsterdam (1989)

Kadanoff L., Lohse D., Wang J., Benzi R.: Scaling and dissipation in the GOY shell model. Phys. Fluids 7(3), 617–629 (1995)

Karatzas I., Shreve S.: Brownian Motion and Stochastic Calculus, 2nd edn. Springer, New York (1991)

L’vov V.S., Podivilov E., Pomyalov A., Procaccia I., Vandembroucq D.: Improved shell model of turbulence. Phys. Rev. E (3) 58(2), 1811–1822 (1998)

Mandrekar V., Rüdiger B.: Existence and uniqueness of pathwise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces. Stochastics 78(4), 189–212 (2006)

Manna U., Sritharan S.S., Sundar P.: Large deviations for the stochastic shell model of turbulence. Nonlinear Differ. Equ. Appl. (NoDEA) 16, 493–521 (2009)

Menaldi J.L., Sritharan S.S.: Stochastic 2-D Navier–Stokes equation. Appl. Math. Optim. 46, 31–53 (2002)

Mueller C.: The heat equation with Lévy noise. Stoch. Process. Appl. 74(1), 67–82 (1998)

Ohkitani K., Yamada M.: Temporal intermittency in the energy cascade process and local Lyapunov analysis in fully developed model of turbulence. Prog. Theor. Phys. 89, 329–341 (1989)

Peszat, S., Zabczyk, J.: Stochastic partial differential equations with Lévy noise. In: Encyclopedia of Mathematics and Its Applications, vol. 113 (2007) Cambridge University Press, Cambridge

Röckner M., Zhang T.S.: Stochastic Evolution Equations of Jump Type: Existence, Uniqueness and Large Deviation Principles. Potential Analysis 26, 255–279 (2007)

Rüdiger B.: Stochastic integration with respect to compensated Piosson randon measures on separable Banach spaces. Stoch. Stoch. Rep. 76(3), 213–242 (2004)

Temam R.: Navier–Stokes Equations, Theory and Numerical Analysis. North-Holland, Amsterdam (1984)

Vishik M.J., Fursikov A.V.: Mathematical Problems of Statistical Hydromechanics. Kluwer Academic Press, Boston (1980)

West, B.J.: An Essay of the Importance Being Non Linear. In: Lecture Notes in Biomathematics, vol. 62. Springer, Berlin (1985)

Zhao D., Chao X.Y.: Global solutions of stochastic 2D Navier–Stokes equations with Lévy noise. Sci. China Ser. A 52(7), 1497–1524 (2009)