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

Author

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  • Peng, Congming
  • Zhao, Dun
  • Shi, Qihong

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<σ

Suggested Citation

  • Peng, Congming & Zhao, Dun & Shi, Qihong, 2023. "Limit of the blow-up solution for the inhomogeneous nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 642-658.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:642-658
    DOI: 10.1016/j.matcom.2022.10.022
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