Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].
Grad, On the kinetic theory of rarefied gases, Comm
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Proves well-posedness of the linearized R13 moment model via 2-by-2 block structure in the LBB saddle-point framework together with new coercivity estimates for symmetric traceless tensor fields.
PINN study of BGK shocks identifies anisotropic tail-weighted observability failure in fourth-order closure R_xx^cl and shows a shock-local correction reduces its relative error to 0.112 using DVM validation.
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Future global stability of Maxwell-J\"uttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes
Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].
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Well-Posedness of the Linear Regularized 13-Moment Equations Using Tensor-Valued Korn Inequalities
Proves well-posedness of the linearized R13 moment model via 2-by-2 block structure in the LBB saddle-point framework together with new coercivity estimates for symmetric traceless tensor fields.
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Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks
PINN study of BGK shocks identifies anisotropic tail-weighted observability failure in fourth-order closure R_xx^cl and shows a shock-local correction reduces its relative error to 0.112 using DVM validation.