Nonlinear PDEs in Continuum Mechanics and Related Topics

Mathematical theory of continuum mechanics gives rise to important classes of nonlinear partial differential equations, such as the celebrated Euler and Navier-Stokes equations for both compressible and incompressible fluids, and Magneto-Hydro-dynamics (MHD) equations for electrically conducting fluids. Understanding solutions to these systems has been crucial in many branches of sciences, such as mechanics, aeronautics, space engineering, geophysics, meteorology, oceanography, and material sciences, etc. The fundamental importance in various applications and great challenge in the theory of nonlinear PDEs of these equations have made them some of the focuses of extensive researches.

Tremendous progress has been made in solving these equations both theoretically and numerically, and in understanding the behavior of solutions to such systems. Yet many problems of fundamental importance still remain open. This workshop aims at bringing together leading and young researchers to exchange the latest trends and developments in the topics of shock waves, boundary layers, fluids free boundary problems, and well-posedness theory of Navier-Stokes equations and MHD equations, among others, and to stimulate the future research in these important fields.