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A UNIFORMLY VALID ASYMPTOTIC THEORY OF RARIFIED GAS FLOWS UNDER THE NEARLY FREEMOLECULE CONDITIONS,
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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An asymptotic theory for obtaining nearly free-molecule solutions which are uniformly valid throughout the flow field of an infinite rarefied gas is proposed in the present study for the linearized Boltzmann equation with hardsphere molecules. Power-law molecules can be treated in a like manner. The theory is based on a new integral formulation of the linearized Boltzmann equation. An inner-and-outer-expansion procedure is used. The simplification in the inner region is that the collisional effects are only secondary while outside of the inner region the angle subtended by the body is small so that the flow field is essentially that created by a source at the origin. In order to examine the mathematical nature of this asymptotic theory, a two-dimensional circular cylinder rotating in a rarefied gas, which is at rest at infinity, is studied. It is proved that the inner and outer solutions obtained by the theory are indeed asymptotic to the true solution throughout the physical space.
APPROVED FOR PUBLIC RELEASE