{"content":[{"text":"Dispersive estimates for the massless Dirac equation \n The solution to the Cauchy problem \n ( \n i@tu + Du = 0, u(t, x) ⇥ R3 \n : Rt ! C4 \n x (1) \n u(0, x) = f(x) \n X 3 \n where D i−1 \n = ↵j@j is the 3D Dirac operator satisﬁes different sets \n j=1 \n of dispersive estimates. \n Strichartz estimates: \n keitDfk . kfkL2, (2) \n 1 1 1 \n Lp ˙H q − p − \n 2 \n t x \n 2 2 \n + = 1, 2 < p  1, 2  q < 1. \n p q \n Applications: crucial tool in the study of nonlinear problems: \n local/global well posedness, scattering... \n Question: do Strichartz estimates hold in presence of perturbations? \n Federico Cacciafesta The Dirac equation in dispersive PDEs CFP 2003 2 / 23","bbox":{"left":0.023438,"top":0.02346,"width":0.959315,"height":0.971313}}],"images_bbox":[{"left":0.057878,"top":0.521817,"width":0.019293,"height":0.025723}],"images_bbox_not_text_overlap":[{"left":0.057878,"top":0.521817,"width":0.019293,"height":0.025723}]}