4 problems
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Entropy–entropy production inequality for the non-cutoff linear Boltzmann equation
Entropy–entropy production conjecture. There exists such that
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The temperature-coupling explanation for Burnett instability
The linearized Burnett system is considered in the BGK setting, where the temperature coupling back to the velocity dynamics has the opposite sign from the stable BGK case. Tempera…
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Regularity conjecture for the grazing-boundary transport problem
Let be a domain with , smooth noncharacteristic boundary away from the grazing set, and suppose the transport problem … has homogeneous inflow da…
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Regularity threshold conjecture for the transport solution
Let , let be the sphere of transport directions, and let denote the interior of the energy interval. Consider the solution…