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L1 Stability of the Boltzmann Equation for the Hard-Sphere Model

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Abstract.

We study the L1 stability of classical solutions to the Boltzmann equation for a hard-sphere model, when initial datum is a small perturbation of a vacuum, and tends to zero exponentially fast at infinity in the phase space. For this, we introduce nonlinear functionals measuring potential interactions between particles with different velocities and L1 distance between classical solutions. We use pointwise estimates for a solution and the gain term of a collision operator to control the time-evolution of nonlinear functionals.

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Authors and Affiliations

  1. School of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea

    Seung-Yeal Ha

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  1. Seung-Yeal Ha
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Correspondence to Seung-Yeal Ha.

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Communicated by T.-P. Liu

Dedicated to Marshall Slemrod on the occasion of his 60th birthday

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Ha, SY. L1 Stability of the Boltzmann Equation for the Hard-Sphere Model. Arch. Rational Mech. Anal. 173, 279–296 (2004). https://doi.org/10.1007/s00205-004-0321-x

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