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GLOBAL EXISTENCE AND STABILITY OF MILD SOLUTIONS TO THE BOLTZMANN SYSTEM FOR GAS MIXTURES

SEUNG-YEAL HA, SE EUN NOH and SEOK BAE YUN
Quarterly of Applied Mathematics
Vol. 65, No. 4 (December 2007), pp. 757-779
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43638798
Page Count: 23
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
GLOBAL EXISTENCE AND STABILITY OF MILD SOLUTIONS TO THE BOLTZMANN SYSTEM FOR GAS MIXTURES
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Abstract

We present the global existence and stability of mild solutions to the Boltzmann system with inverse power molecular interactions for a binary gas mixture, when initial data are sufficiently small and decay exponentially in phase space. For the existence and stability of mild solutions, we employ a modified Kaniel-Shinbrot's scheme and a weighted nonlinear functional approach. Time-asymptotic convergence toward the free molecular motion is established using a weighted collision potential, and we show that the weighted L¹ -distance between two mild solutions is uniformly controlled by that of initial data.

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