On A Priori Estimates for Rough PDEs
In this note, we present a new and simple method which allows to get a priori bounds on rough partial differential equations. The technique is based on a weak formulation of the equation and a rough version of Gronwall’s lemma. The method is presented on a simple linear example, but might be generalized to a wide number of situations.
KeywordsA priori estimate Rough Gonwall lemma Rough paths Stochastic PDEs
- 1.I. Bailleul, M. Gubinelli, Unbounded rough drivers (2015). arXiv:1501.02074Google Scholar
- 3.L. Chen, Y. Hu, K. Kalbasi, D. Nualart, Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise (2016). arXiv:1602.05617Google Scholar
- 6.A. Deya, M. Gubinelli, M. Hofmanova, S. Tindel, General a priori estimates for rough PDEs with applications to rough conservation laws (2016). arXiv:1604.00437Google Scholar
- 10.M. Gubinelli, P. Imkeller, N. Perkowski, Paracontrolled distributions and singular PDEs. Forum Math. Pi 3(e6), 75 (2015)Google Scholar
- 11.M. Gubinelli, S. Tindel, I. Torrecilla, Controlled viscosity solutions of fully nonlinear rough PDEs (2014). arXiv:1403.2832Google Scholar