Regularization by noise and stochastic Burgers equations

Massimiliano Gubinelli1, Milton Jara2
1CEREMADE UMR 7534, Université Paris-Dauphine, Paris, France
2IMPA, Estrada Dona Castorina 110, Rio de Janeiro, CEP 22460-320, Brazil

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Albeverio, S., Cruzeiro, A.-B.: Global flows with invariant (Gibbs) measures for Euler and Navier–Stokes two dimensional fluids. Commun. Math. Phys. 129(3), 431–444 (1990). doi: 10.1007/BF02097100

Albeverio S., Ferrario B.: Some Methods of Infinite Dimensional Analysis in Hydrodynamics: An Introduction, SPDE in Hydrodynamic: Recent Progress and, Prospects, Cetraro, pp. 1–50 (2008)

Assing, S.: A pregenerator for Burgers equation forced by conservative noise. Commun. Math. Phys. 225(3), 611–632 (2002). doi: 10.1007/s002200100606

Assing S.: A rigorous equation for the Cole–Hopf solution of the conservative KPZ dynamics. arXiv:1109.2886 (2011)

Babin, A.V., Ilyin, A.A., Titi, E.S.: On the regularization mechanism for the periodic Korteweg-de Vries equation. Commun. Pure Appl. Math. 64(5), 591–648 (2011). doi: 10.1002/cpa.20356

Babin, A., Mahalov, A., Nicolaenko, B.: Regularity and integrability of $$3$$ D Euler and Navier–Stokes equations for rotating fluids. Asymptot. Anal. 15(2), 103–150 (1997)

Bertini, L., Giacomin, G.: Stochastic Burgers and KPZ equations from particle systems. Commun. Math. Phys. 183(3), 571–607 (1997). doi: 10.1007/s002200050044

Chang, C.-C., Landim, C., Olla, S.: Equilibrium fluctuations of asymmetric simple exclusion processes in dimension $$d\ge 3$$ . Probab. Theory Relat. Fields 119(3), 381–409 (2001). doi: 10.1007/PL00008764

Da Prato G., Debussche A., Tubaro L.: A modified Kardar–Parisi–Zhang model. Electron. Commun. Probab. 12, 442–453 (2007)

Da Prato, G., Flandoli, F.: Pathwise uniqueness for a class of SDE in Hilbert spaces and applications. J. Funct. Anal. 259(1), 243–267 (2010). doi: 10.1016/j.jfa.2009.11.019

Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications, vol. 44. Cambridge University Press, Cambridge (1992)

Flandoli, F., Gubinelli, M., Priola, E.: Well-posedness of the transport equation by stochastic perturbation. Invent. Math. 180(1), 1–53. doi: 10.1007/s00222-009-0224-4 (2010)

Flandoli, F., Russo, F., Wolf, J.: Some SDEs with distributional drift. I. General calculus. Osaka J. Math. 40(2), 493–542 (2003)

Flandoli, F., Russo, F., Wolf, J.: Some SDEs with distributional drift. II. Lyons–Zheng structure, Itô’s formula and semimartingale characterization. Random Oper. Stoch. Equ. 12(2), 145–184 (2004). doi: 10.1163/156939704323074700

Gonçalves P., Jara M.: Universality of KPZ equation, arXiv:1003.4478 (2010)

Gubinelli, M.: Controlling rough paths. J. Funct. Anal. 216(1), 86–140 (2004). doi: 10.1016/j.jfa.2004.01.002

Gubinelli, M.: Rough solutions for the periodic Korteweg-de Vries equation. Commun. Pure Appl. Anal. 11(2), 709–733 (2012)

Hairer, M.: Solving the KPZ equation, ArXiv (2011)

Janson, S.: Gaussian Hilbert Spaces. Cambridge University Press, Cambridge (1997)

Kardar, M., Parisi, G., Zhang, Y.-C., Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56(9), 889–892 (1986). doi: 10.1103/PhysRevLett.56.889

Kipnis, C., Varadhan, S.R.S.: Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Commun. Math. Phys. 104(1), 1–19

Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion, 3rd edn. Springer, Heidelberg (2004)

Russo, F., Trutnau, G.: Some parabolic PDEs whose drift is an irregular random noise in space. Ann. Probab. 35(6), 2213–2262 (2007). doi: 10.1214/009117906000001178

Russo, F., Vallois, P.: Elements of Stochastic Calculus via Regularization, Séminaire de Probabilités XL, pp. 147–185. Springer, Berlin (2007)

Sasamoto, T., Spohn, H.: Superdiffusivity of the 1D Lattice Kardar–Parisi–Zhang equation. J. Stat. Phys. 137(5), 917–935 (2009). doi: 10.1007/s10955-009-9831-0