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Hyperbolic & Dispersive PDE Seminar

Local smoothing for the wave equation in 2 + 1 dimensions

Ruixiang Zhang (UC Berkeley)

Location:  Hill 525
Date & time: Thursday, 08 December 2022 at 2:00PM - 3:00PM

Sogge's local smoothing conjecture for the wave equation predicts that the local $$L^p$$ space-time estimate gains a fractional derivative of order almost $$1/p$$ compared to the fixed time $$L^p$$ estimates, when $$p>2n/(n-1)$$. Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $$bb{R}^{2+1}$$. I will talk about our proof and explain several important ingredients such as induction on scales and an incidence type theorem.