We will give an introduction to Fourier multiplier techniques for the solution of nonlinear partial differential equations in unbounded domains, starting from very simple models on the real line.
We will then move on to discuss several examples of recent work where such techniques have been crucial for the construction of solutions.
We finally discuss the use of solutions constructed with these techniques for proving uniqueness of weak solutions.
Throughout the course we will present open questions that should be accessible to a discussion with the methods introduced during the course.