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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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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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.