Conservation laws and symmetrization of the equations of incompressible inviscid fluids

Author:
Lubin G. Vulkov

Journal:
Quart. Appl. Math. **57** (1999), 549-560

MSC:
Primary 35L65; Secondary 76B99

DOI:
https://doi.org/10.1090/qam/1704427

MathSciNet review:
MR1704427

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Abstract: Many physical processes are described by conservative quasilinear systems of equations that admit a supplementary independent conservation law. A typical example is the equations of incompressible fluid dynamics. If for basic equations the conservation laws of the momentum and the volume are chosen then the conservation law of the energy is an additional conservation law. In the present paper all conservation laws for incompressible fluid dynamics are derived and the symmetric forms of its equations are obtained. Godunov's method of symmetrization is generalized for the case of an arbitrary quasilinear system of equations.

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DOI:
https://doi.org/10.1090/qam/1704427

Article copyright:
© Copyright 1999
American Mathematical Society