The course aims to provide an introduction to the theory of initial boundary value problems for Friedrichs symmetrizable systems, with particular interest for the applications to the equations of ideal Magneto-Hydrodynamics (MHD).
We first analyse different kinds of boundary conditions and present the main results about the well-posedness. In the case of the characteristic boundary, we discuss the possible loss of regularity in the normal direction to the boundary and the use of suitable anisotropic Sobolev spaces in MHD.
Finally, we give a short introduction to the Kreiss-Lopatinskii approach and discuss a simple boundary value problem for the wave equation that may admit estimates with a loss of derivatives from the data.
Further Information
This course is running as part of the National PDE Network Meeting being held in Oxford 18-21 March 2024, and jointly with the 13th Oxbridge PDE conference.
The course is broken into 3 sessions over two days, thus, with all sessions taking place in L2:
In this short course, we will discuss the Euler equations and applications in gas dynamics and geometry. First, the basic theory of Euler equations and mixed-type problems will be reviewed. Then we will present the results on the transonic flows past obstacles, transonic flows in the fluid dynamic formulation of isometric embeddings, and the transonic flows in nozzles. We will discuss global solutions and stability obtained through various techniques and approaches. The short course consists of three parts and is accessible to PhD students and young researchers.
Further Information
This course is running as part of the National PDE Network Meeting being held in Oxford 18-21 March 2024, and jointly with the 13th Oxbridge PDE conference.
The course is broken into 3 sessions over two days, with all sessions taking place in L2:
