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Contenido archivado el 2022-12-23

Strong solutions and numerical applications for the Navier-Stokes System

Objetivo



The Navier-Stokes system describes the motion of incompressible fluids and is one of the most difficult non-linear systems of partial differential equations in mathematical physics. On the other hand, one cannot overestimate the significance of the problems related to this system because of its numerous applications in science, industry and other aspects of life.

The existence and uniqueness theorems, as well as different numerical methods for finding solutions of this system, attract many mathematical and mechanical schools. Recently, a group at the University of Stuttgart, with the help of scientists from St. Petersburg University and St. Petersburg Electrotechnical University, have obtained some new pointwise estimates for strong solutions of the Navier-Stokes system. These results pave the way for a new approach in the application of different approximation methods for solving some three-dimensional problems.

New theoretical results for strong solutions are also expected. These numerical methods will be: the variational-difference methods used in St. Petersburg; finite element approximations and corresponding robust multi-grid methods and filtering decompositions; coupled variational boundary integral equation methods with finite and boundary elements (both in Stuttgart); approximate approximations in Linkoping.

Since pressure and velocity governed by the Navier-Stokes equations develop singularities at non-regular boundary points, corresponding asymptotic expansions near vertex and edge points will be considered with various boundary conditions. The research on expansions near a vertex will be based on a detailed analysis of the spectrum of operator pencils associated with the Stokes system in the cone.

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Coordinador

Universität Stuttgart
Aportación de la UE
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Dirección
Pfaffenwaldring 57
70569 Stuttgart
Alemania

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Participantes (3)