Quasiconformal mappings and problems in hydrodynamics
Abstract
A review of Lavrentiev's works in the theory of quasiconformal mapping and motions of ideal liquids with finite boundaries is presented. The 'L-elliptical' equations which describe complex processes of hydrodynamics, such as subsonic steady-state flow of ideal gases and liquid filtration in inhomogeneous anisotropic porous media are considered; problems of conformal and quasiconformal identification are examined. Finally, methods of harmonic mapping, the application of Cauchy-Riemann expressions to the mapping of three-dimensional regions, and the Lavrentiev wave theory are discussed.
- Publication:
-
PMTF Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki
- Pub Date:
- March 1981
- Bibcode:
- 1981PMTF...21...59M
- Keywords:
-
- Computational Fluid Dynamics;
- Conformal Mapping;
- Hydrodynamics;
- Ideal Fluids;
- Cauchy-Riemann Equations;
- Free Boundaries;
- Gas Dynamics;
- Harmonic Analysis;
- Subsonic Flow;
- Fluid Mechanics and Heat Transfer