Applications of mathematics in astrophysical hydrodynamics

The aim of the seminar is to present approaches and problems that arise in the analysis of dynamics of planetary and stellar fluid interiors. This involves the convective heat transfer in the presence of density stratification and the hydromagnetic dynamo effect. Moreover, development of magnetohydrodynamic instabilities determines the dynamics of the natural magnetic fields and in particular the detailed analysis of the so-called Solar tachocline - a region with strong shear in the Solar inetrior, is crucial for understanding of the Sun's activity and magnetic storms on the Earth. Therefore the seminar will involve a short description of the equations used to model heat transfer and the dynamo effects in the Earth's core and of the equations describing the Solar tachocline. Moreover, particular unanswered problems which require mathematical tools will be described.

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