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Formation of condensations for non-radial solutions to 3-wave kinetic equations

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arxiv 2503.17066 v1 pith:QZKJUYH6 submitted 2025-03-21 math.AP

Formation of condensations for non-radial solutions to 3-wave kinetic equations

classification math.AP
keywords solutionsbose-einsteincondensatestimecasecirclesdiracdirection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider in this work a $2$-dimensional $3$-wave kinetic equation describing the dynamics of the thermal cloud outside a Bose-Einstein Condensate. We construct global non-radial mild solutions for the equation. Those mild solutions are the summation of Dirac masses on circles. We prove that in each spatial direction, either Dirac masses at the origin, which are the so-called Bose-Einstein condensates, can be formed in finite time or the solutions converge to Bose-Einstein condensates as time evolves to infinity. We also describe a dynamics of the formation of the Bose-Einstein condensates latter case. In this case, on each direction, the solutions accumulate around circles close to the origin at growth rates at least linearly in time.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 conditional novelty 8.0

    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.

  2. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 unverdicted novelty 7.0

    New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.

  3. Spectral Algorithms for 3-Wave Kinetic and $C_{12}$ Quantum Boltzmann Equations with General Resonance Manifolds in $\mathbb{R}^d$

    math.NA 2026-08 conditional novelty 6.0

    A fast FFT-based spectral method computes 3-wave kinetic and C12 quantum Boltzmann collision operators in O(L(2N)^{2d} log(2N)) operations and shows apparent energy cascades in non-radial 3D simulations.

  4. Global time-analytic strong solutions for a class of 3-wave kinetic equations

    math-ph 2026-07 accept novelty 6.0

    For radial nonnegative data, a regularized 3-wave kinetic equation has a unique global strong solution that stays nonnegative and is time-analytic.