@inproceedings{8a7621139007499a976815e8a7930c02,

title = "Damped Nonlinear Schr{\"o}dinger Equation with Stark Effect",

abstract = "The problem of singularity formation for damped NLS (dNLS) has been an interesting and meanwhile challenging one in both mathematical and physical literature. We study the L2-critical damped NLS with a Stark potential. We prove that the threshold for global existence and finite time blow-up of this equation is given by Q2, where Q is the unique positive radial solution of ΔQ+|Q|4/dQ=Q in H1(Rd). Moreover, in any small neighborhood of Q, there exists an initial data u0 above the ground state such that the solution flow admits the log-log blow-up speed. This verifies the structural stability for the “log-log law” associated to the NLS mechanism under the perturbation by a damping term and a Stark potential. The proof of our main theorem is based on the Avron-Herbst formula and the analogous result for the unperturbed dNLS. The method of our analysis allows to further prove a general blow-up criterion. Moreover, we give a concentration compactness description for the limiting behavior of blow-up solutions, which might have independent analytical interest.",

keywords = "35B40, 35Q55, Avron-Herbst formula, Damped nonlinear Schr{\"o}dinger equation, Stark potential",

author = "Yi Hu and Yongki Lee and Shijun Zheng",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 6th International Workshop on Nonlinear and Modern Mathematical Physics, NMMP 2022 ; Conference date: 17-06-2022 Through 19-06-2022",

year = "2024",

doi = "10.1007/978-3-031-59539-4_7",

language = "English",

isbn = "9783031595387",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "189--205",

editor = "Solomon Manukure and Wen-Xiu Ma",

booktitle = "Nonlinear and Modern Mathematical Physics - NMMP-2022",

address = "Germany",

}