slideshow 3

Seminar on partial differential equations

Compressible nonlinearly viscous fluids: Asymptotic analysis in a 3D curved domain

Richard Andrášik
Palacký University Olomouc


Tuesday, 17. December 2019 - 9:00 to 10:00

in IM, rear building, ground floor

Governing equations representing mathematical description of continuum mechanics have often three spatial dimensions and one temporal dimension. However, their analytical solution is usually unattainable, and numerical approximation of the solution unduly complicated and computationally demanding. Thus, these models are frequently simplified in various ways. One option of a simplification is a reduction of the number of spatial dimensions. Nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a three-dimensional domain were considered. These equations need a simplification, when possible, to be effectively solved. Therefore, a dimension reduction was performed for this type of a model. Dynamics of a compressible fluid in thin domains was studied. The current framework was extended by dealing with nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a deformed three-dimensional domain where only two dimensions are dominant. The deformation of a domain introduced new difficulties in the asymptotic analysis, because it affects the limit equations in a non-trivial way. However, these challenges were addressed, and the two-dimensional model was rigorously derived.