Accession Number : AD0682225

Title :   ON THE LINEARIZATION OF THE EQUATIONS OF HYDRODYNAMICS,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Sattinger,D. H.

Report Date : 1965

Pagination or Media Count : 39

Abstract : The basic problem in hydrodynamic stability is to determine the critical values of the Reynolds number at which the flow becomes unstable. As the equations are nonlinear, it is hard to get any meaningful quantitative information (i.e. numbers) from a direct analysis of them. Accordingly much of the literature in hydrodynamic stability is devoted to an analysis of linearized equations. It is argued that if the perturbations are small then the nonlinear term is of second order magnitude and can be neglected. Of course, this argument is open to question, especially as the nonlinear term involves derivatives of the flow, which may not be small. Nevertheless, a considerable body of experimental evidence tends to support this 'linearization hypothesis,' and the point of this paper is to give a rigorous, general mathematical proof of its validity in the case of a bounded domain. (Author)

Descriptors :   (*INCOMPRESSIBLE FLOW, STABILITY), (*NONLINEAR DIFFERENTIAL EQUATIONS, *PERTURBATION THEORY), NAVIER STOKES EQUATIONS, CALCULUS OF VARIATIONS, HILBERT SPACE, NUMERICAL INTEGRATION, THEOREMS

Subject Categories : Theoretical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE