Well/Ill-Posedness of the Boltzmann Equation with Soft Potential

Well/Ill-Posedness of the Boltzmann Equation with Soft Potential

We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs Sobolev space. We find the well/ill-posedness separation at regularity s=d-12, strictly 12-derivative highe...

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Veröffentlicht in:Communications in mathematical physics 2024-12, Vol.405 (12), Article 283
Hauptverfasser: Chen, Xuwen, Shen, Shunlin, Zhang, Zhifei
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Boltzmann transport equation
Ill posed problems
Separation
Sobolev space
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description We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs Sobolev space. We find the well/ill-posedness separation at regularity s=d-12, strictly 12-derivative higher than the scaling-invariant index s=d-22, the usually expected separation point.
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subjects Boltzmann transport equation
Ill posed problems
Separation
Sobolev space
title Well/Ill-Posedness of the Boltzmann Equation with Soft Potential
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