ncku-talk2013-04-18

NCTS(South)/ NCKU Math Colloquium

DATE 2013-04-18　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 吳恭儉博士 (Dr. Kung-Chien Wu)（英國劍橋大學純粹數學與數理統計系 (Dept. of Pure Math. and Math. Stat., Univ. of Cambridge, UK) ）

TITLE Wave Structures of the Linearized Boltzmann Equation in a Periodic Box

ABSTRACT We study the wave structures of the linearized Boltzmann equation in a periodic box for non-smooth initial perturbations.
The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, and the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. The iterated averaging lemma plays an important role in constructing the kinetic-like waves. We also supply some new ideas of this lemma.

NCTS(South)/ NCKU Math Colloquium

DATE	2013-04-18　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	吳恭儉博士 (Dr. Kung-Chien Wu)（英國劍橋大學純粹數學與數理統計系 (Dept. of Pure Math. and Math. Stat., Univ. of Cambridge, UK) ）

TITLE	Wave Structures of the Linearized Boltzmann Equation in a Periodic Box

ABSTRACT	We study the wave structures of the linearized Boltzmann equation in a periodic box for non-smooth initial perturbations. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, and the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. The iterated averaging lemma plays an important role in constructing the kinetic-like waves. We also supply some new ideas of this lemma.