Unbounded Rough Drivers and the Variational Approach to Rough Partial Differential Equations
A framework for solving partial differential equations forced by irregular-in-time signals, in which the driving term is modeled as an unbounded rough driver: a rough path taking values in unbounded linear operators on a scale of Banach spaces. Learners study the variational (energy-estimate) approach and its analytic backbone (controlled rough paths, the Sewing lemma, and a rough Gronwall inequality) to prove well-posedness of parabolic rough PDEs and to treat concrete transport-noise models such as Landau-Lifshitz-Gilbert, Navier-Stokes, and Euler equations.
Unbounded rough drivers, rough PDEs and applications Antoine Hocquet
A review article surveying recent progress on rough partial differential equations (RPDEs) driven by low-time-regularity signals, organized around the formalism of the unbounded rough driver: a rough…