Diffusions with Rough Drifts and Stochastic Symplectic Maps

Wed, Mar 4, 2015, 3:00 pm

This is a joint seminar with the Probability Seminar. Please note special day and time.  According to DiPerna-Lions theory, velocity fields with weak derivatives in Lp spaces possess weakly regular flows. When a velocity field is perturbed by a white noise, the corresponding (stochastic) flow is far more regular in spatial variables; a d-dimensional diffusion with a drift in Lr,q space (r for the spatial variable and q for the temporal variable) possesses weak derivatives with stretched exponential bounds, provided that d/r+2/q<1. As an application one show that a Hamiltonian system that is perturbed by a white noise produces a symplectic flow provided that the corresponding Hamiltonian function H satisfies ∇HLr,q with d/r+2/q<1. As our second application we derive a Constantin-Iyer type circulation formula for certain weak solutions of Navier-Stokes equation.

Location: 
Fine 322
Speaker(s): 

Upcoming Events

PACM Colloquium, Prof. Lin Lin, UC Berkeley University

Mon, Feb 6, 2023, 4:30 pm
Location: 214 Fine Hall

ANALYSIS OF FLUIDS AND RELATED TOPICS: Kevin Zumbrun, Indiana University

Thu, Feb 9, 2023, 3:00 pm
Location: Fine Hall 314

GRADUATE STUDENT SEMINAR, Pinchen Xie

Mon, Feb 13, 2023, 12:30 pm
Location: Fine Hall 214