Fachbereich Mathematik

Non-Linear Dispersive Partial Differential Equations


  • To know basic and advanced tools of Fourier analysis, and their application to the study of nonlinear partial differential equations;
  • To be able to investigate local and global well-posedness for the Cauchy problem of semi- and quasi-linear Wave and Schrödinger equations;
  • To understand the physical relevance of nonlinear partial differential equations.


  • Basic tools of Fourier analysis (Inequalities, Sobolev spaces and their embeddings);
  • Littlewood-Paley theory, Besov spaces;
  • Notions of solution of a (nonlinear) partial differential equation, boundary and initial value problems;
  • Fixed point arguments, conservation laws, and energy method;
  • TT* argument and Strichartz estimates;
  • Applications to nonlinear dispersive equations: Wave and Schrödinger equations.

Suggested Bibliography


Freely available online lecture notes


  • Exercise Classes and Homework

One exercise class / complementary lecture per week. The homework assignments will be given biweekly. Half of the total homework points are required to be admitted to the final exam.

  • Final Exam

The final examination will be an oral verification of the knowledge acquired during the course.