Global well-posedness for the Boltzmann equation near vacuum holds in anisotropic Besov spaces with critical regularity index 2/p.
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Applies l²-decoupling to derive Strichartz and space-time bilinear estimates that imply unconditional uniqueness for the Boltzmann equation on R^d and T^d under Maxwellian/soft potentials with angular cutoff.
Direct construction establishes strong-weak ill-posedness for the hard-sphere Boltzmann equation in H_x^s when s<1, completing the sharp regularity threshold with well-posedness for s>1.
citing papers explorer
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Low-regularity global well-posedness for the Boltzmann equation near vacuum
Global well-posedness for the Boltzmann equation near vacuum holds in anisotropic Besov spaces with critical regularity index 2/p.
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$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation
Applies l²-decoupling to derive Strichartz and space-time bilinear estimates that imply unconditional uniqueness for the Boltzmann equation on R^d and T^d under Maxwellian/soft potentials with angular cutoff.
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Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation
Direct construction establishes strong-weak ill-posedness for the hard-sphere Boltzmann equation in H_x^s when s<1, completing the sharp regularity threshold with well-posedness for s>1.