School and Conference on Modern Mathematical Physics

9 - 14 September 2019, Belgrade, Serbia


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    E-mail: mphys10@ipb.ac.rs


Marcelo Enrique Rubio

On well-posedness of non-linear theories in mathematical physics

One of the most challenging purposes of theoretical physics is to develop theories that attempt to explain and understand, as accurately as possible, the evolution of physical systems given a certain initial configuration. This aspect is crucial and inevitable in order to guarantee the predictability power of the theory. The theory of partial differential equations provides results and powerful tools to study this problem, which is known as the Cauchy problem or initial value problem. Although functional analysis helps to formalize several aspects associated with the functional spaces in which the existence, uniqueness and continuity of the evolution with respect to the initial data is guaranteed, there is a series of purely algebraic tools that univocally characterize well-posed systems.

In this talk we will review some motivational and relevant results when approaching and studying the initial value problem in physics, and after commenting on open problems and difficulties that appear, we will illustrate their use for the study of non-linear relativistic extensions of classical theories such as electromagnetism and hydrodynamics.


Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Faculty of Mathematics (University of Belgrade)
Belgrade, Serbia
Mathematical Institute (Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Faculty of Science (University of Kragujevac)
Kragujevac, Serbia


Serbian Academy of Sciences and Arts (SASA)
Belgrade, Serbia

Institute of Nuclear Sciences "VinĨa" (University of Belgrade)
Belgrade, Serbia
Institute of Physics (University of Kragujevac)
Kragujevac, Serbia

Faculty of Physics (University of Belgrade)
Belgrade, Serbia
Faculty of Sciences (University of Novi Sad)
Novi Sad, Serbia
School of Electrical Engineering (University of Belgrade)
Belgrade, Serbia

SEENET-MTP (Southeastern European Network in Mathematical and Theoretical Physics)
Nis, Serbia