Global solutions with heat-like decay and Gevrey regularity propagation are proven for the Boltzmann equation in half-space with zero Mach number at infinity.
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A counterexample demonstrates that entropy production is not always monotone decreasing for the space-homogeneous Boltzmann equation with a non-standard collision kernel, disproving McKean's conjecture.
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Half-space problem on the Boltzmann equation with zero Mach number at infinity
Global solutions with heat-like decay and Gevrey regularity propagation are proven for the Boltzmann equation in half-space with zero Mach number at infinity.
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The entropy production is not always monotone in the space-homogeneous Boltzmann equation
A counterexample demonstrates that entropy production is not always monotone decreasing for the space-homogeneous Boltzmann equation with a non-standard collision kernel, disproving McKean's conjecture.