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A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem

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  • We present a Fourier transform formula of quadratic-form type for the collision operator with a Maxwellian kernel under the momentum transfer condition. As an application, we extend the work of Toscani and Villani on the uniform stability of the Cauchy problem for the associated Boltzmann equation to any physically relevant Maxwellian molecules in the long-range interactions with a minimal requirement for the initial data.
    Mathematics Subject Classification: 35Q82, 47G20, 76P05, 82B40.


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