Five open problems in compressible mathematical fluid dynamics

Five Open Problems in Compressible Mathematical Fluid Dynamics

The problems below are motivated by some of the works I did in the past. They deal with the dynamics of compressible fluids, either viscous or inviscid. They could be good questions for mathematicians having originality and technical strength. They are not worth a million dollars, even not a penny, but they are interesting in their own. 1 Global-in-time Cauchy problem for Euler–Fourier system P...

Open problems in mathematical physics

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recen...

The dynamics of viscous compressible fluid in a fracture

We solve a problem of fluid dynamics in an arbitrarSignificant progress has been made in the quantitative ily shaped fracture containing proppant. The fracture modeling of the dynamic interaction of a fracture with is embedded in an absolutely rigid solid. The fluid flow surrounding elastic rock. Using the finite-difference method, is induced by normal harmonic oscillations of fracture Chouet (...

Open Problems in Symbolic Dynamics

Open Problems in Logical Dynamics

In recent years, a number of 'dynamic epistemic logics' have been developed for dealing with information, communication, and interaction. This paper is a survey of conceptual issues and open mathematical problems emanating from this development. 1 Logical Dynamics The traditional paradigm of logic is drawing a conclusion from some given premises. But derivation from data already at our disposal...