Global well-posedness and critical norm concentration for inhomogeneous biharmonic NLS

Author(s)

Cardoso, Mykael ^[1] ; Guzman, Carlos M. ^[2] ; Pastor, Ademir ^[3]

Affiliation

^[1] Univ Fed Piaui, Dept Math, Teresina - Brazil

^[2] UFF, Dept Math, Rio De Janeiro - Brazil

^[3] IMECC UNICAMP, AfAEo Paulo, Dept Math, Afaeo Paulo - Brazil

• Document type: Journal article
• Source: MONATSHEFTE FUR MATHEMATIK; JAN 2022.
• Web of Science Citations: 0

Abstract

We consider the inhomogeneous biharmonic nonlinear Schr o dinger (IBNLS) equation in R-N, i partial derivative(t)u + Delta(2)u - vertical bar x vertical bar(-b)vertical bar u vertical bar(2 sigma) u = 0, where sigma > 0 and b > 0. We first study the local well-posedness in (H)over dot(sc) boolean AND (H)over dot(2), for N >= 5 and 0 < s(c) < 2, where s(c) = N/2 - 4-b/2 sigma. Next, we established a Gagliardo-Nirenberg type inequality in order to obtain sufficient conditions for global existence of solutions in (H)over dot(sc) boolean AND (H)over dot(2) with 0 <= s(c) < 2. Finally, we study the phenomenon of L-sigma c-norm concentration for finite time blow up solutions with bounded (H)over dot(sc)-norm, where sigma(c) = 2N sigma/4-b. Our main tool is the compact embedding of (L)over dot(p) boolean AND (H)over dot(2) into a weighted L2 sigma+2 space, which may be seen of independent interest. (AU)

• FAPESP's process: 19/02512-5 - Systems and partial differential equations
• Grantee: Marcelo da Silva Montenegro
• Support Opportunities: Research Projects - Thematic Grants