M0997 Reading seminar: Nonlinear Schrödinger equations

Faculty of Science
Autumn 2024
Extent and Intensity
0/1/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
doc. Phuoc Tai Nguyen, PhD (lecturer)
Guaranteed by
doc. Phuoc Tai Nguyen, PhD
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 10:00–10:50 MS1,01016
Prerequisites
Calculus of multiple variables, Linear Algebra, Functional analysis, Ordinary differential equations, Partial di erential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The reading seminar aims to establish a forum for students to explore and delve into the theory of linear and nonlinear Schrödinger equations. In particular, students will learn several mathematical tools to investigate the global existence and finite time blowup of solutions to nonlinear Schrödinger equations. This will be implemented through discussions and seminar presentations.
Learning outcomes
By the end of the reading seminar, students should have acquired knowledge of recent developments, mastery of various methods and techniques, and the ability to effectively present research papers in the theory of nonlinear Schrödinger equations. These competencies are important for pursuing independent research in this field.
Syllabus
  • The seminar will tentatively cover the following topics:
  • theory of linear Schrödinger equations,
  • local existence for the Cauchy problem for nonlinear Schrödinger equations,
  • global existence and finite time blowup,
  • nonlinear Schrödinger equations with nonlocal nonlinear term,
  • nonlinear Schrödinger equations with singular potentials.
Literature
  • Elek Csobo and Franois Genoud, Minimal mass blow-up solutions for the L2 critical NLS with inverse-square potential, Nonlinear Anal. 168 (2018), 110{129.
  • Terence Tao, Nonlinear dispersive equations, CBMS Reg. Conf. Ser. Math., 106 Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006, xvi+373 pp.
  • Thierry Cazenave, Semilinear Schrodinger equations, Courant Lect. Notes Math., 10 New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003, xiv+323 pp.
  • Debangana Mukherjee, Phan Thanh Nam and Phuoc-Tai Nguyen, Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential, J. Funct. Anal. 281 (2021), no. 5, Paper No. 109092, 45 pp.
Teaching methods
Students' reports and presentation with a discussion.
Assessment methods
Evaluation of an activity.
Language of instruction
English
Further Comments
Study Materials
The course is taught only once.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/M0997