This volume presents a series of lectures given at the Winter School in Fluid Dynamics held in Paseky, Czech Republic in December 1993. Including original research and important new results, it contains a detailed investigation of some methods used towards the proof of global regularity for the Navier-Stokes equations. It also explores new formulations of the free-boundary in the dynamics of viscous fluids, and different methods for conservation laws in several space dimensions and related numerical schemes. The final contribution examines the existence and stability of non-isothermal compressible fluids and their relation with incompressible models.
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This volume consists of four papers that are based on a series of lectures delivered by the authors at the Third Winter School in Fluid Dynamics, held in Paseky Czech Republic, in December 12 - December 18, 1993. They concern different fields of theoretical and computational fluid mechanics. The paper of Heywood gives various views on the Navier-Stokes theory, for their relation to the problem of the global existence of smooth solutions. The contribution of Kazhikov is dedicated to some new statements of the initial boundary value problems for Navier-Stokes equations of viscous gas while the paper of Kroner surveys recent results and developments for upwind finite volume methods for conservation laws on unstructured grids. Finally, the paper of Padula concerns the existence, stability and asymptotic behaviour theory for different motions of viscous compressible fluids.
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