The leading-order asymptotic behavior of the two-point correlation function for a weakly interacting Fermi gas at kinetic times is exactly the collisional frequency of the equilibrium Boltzmann-Nordheim collision operator.
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For a broad class of 3-wave kinetic equations, a new one-sided entropy mechanism yields global L^1_loc weak solutions and forces local relaxation to zero as t tends to infinity.
For radial nonnegative data, a regularized 3-wave kinetic equation has a unique global strong solution that stays nonnegative and is time-analytic.
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On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
The leading-order asymptotic behavior of the two-point correlation function for a weakly interacting Fermi gas at kinetic times is exactly the collisional frequency of the equilibrium Boltzmann-Nordheim collision operator.
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Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations
For a broad class of 3-wave kinetic equations, a new one-sided entropy mechanism yields global L^1_loc weak solutions and forces local relaxation to zero as t tends to infinity.
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Global time-analytic strong solutions for a class of 3-wave kinetic equations
For radial nonnegative data, a regularized 3-wave kinetic equation has a unique global strong solution that stays nonnegative and is time-analytic.