Seminar:
Analysis
Event time:
Thursday, November 9, 2023 - 4:00pm
Speaker:
Ryan McConnell
Speaker affiliation:
UIUC
Event description:
The second member of the Korteweg-de Vries hierarchy (2KdV) on the Torus is given by
{ut−∂5xu+α∂x(u3)+β∂x(∂xu)2+γ∂x(u∂2xu)=0u(x,0)=u0∈Hs(T),
for (α,β,γ)=(−10,5,10) and u0 real valued. For this choice of coefficients, the equation is known to be completely integrable and wellposed in L2(T) (Kappeler \& Molnar, 2018). In this talk, we’ll provide context and discuss the proof wellposedness for s>35/64, unconditional wellposedness for s>1, and nonlinear smoothing of order ε<min(2(s−35/64),1), which states that the nonlinear evolution is, up to a phase rotation of the linear evolution, in Hs+ε(T). In fact, our methods apply to more general coefficients, where the best known prior results only establish wellposedness for s≥3/2 (Kato, ‘18).