2020/01/24 by Seungly Oh, Oh, Seungly, Atanas Stefanov +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2001.08984
For generalized KdV models with polynomial nonlinearity, we establish nonlinear smoothing property in Hs for s>(1)/(2). Such smoothing effect persists globally, provided that the H1 norm does not blow up in finite time. More specifically, we show that a translate of the nonlinear part of the solution gains min(2s-1,1)- derivatives for s>(1)/(2). Following a new simple method, which is of independent interest, we establish that, for s>1, Hs norm of a solution grows at most by ⟨ t⟩s-1+ if H1 norm is a priori controlled.