Limit of the blow-up solution for the inhomogeneous nonlinear Schrödinger equation

Congming Peng, Dun Zhao and Qihong Shi

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 642-658

Abstract: We study the H1 blow-up profile for the inhomogeneous nonlinear Schrödinger equation i∂tu=−Δu−|x|k|u|2σu,(t,x)∈R×RN,where k∈(−1,2N−2) and N≥3. We develop a new version of Gagliardo–Nirenberg inequality for σ∈[2+kN,2+kN−2] and k∈(−1,2N−2), and show that for the L2-critical exponent σ=2+kN, u(t) has no L2-limit as t→T∗ when ‖u(t)‖H1 blows up at T∗. Moreover, we investigate L2 concentration at the origin in the radial case. Additionally, if 2+kN<σKeywords: Blow up; Inhomogeneous nonlinear Schrödinger equation; L2-concentration (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:642-658

DOI: 10.1016/j.matcom.2022.10.022

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