»ã±¨±êÌâ (Title)£ºSpace-time structure and particle-fluid duality of solutions for the Boltzmann equation with hard potentials

£¨Ó²ÊÆBoltzmann·½³Ì½âµÄʱ¿Õ½á¹¹ÓëÁ£×Ó-Á÷Ìå¶Ôż£©

»ã±¨ÈË (Speaker)£º Íõº£ÌÎ ½ÌÊÚ£¨ÉϺ£½»Í¨´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê11ÔÂ13ÈÕ£¨ÖÜËÄ£©15:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÍõÓî³Î

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»ã±¨ÌáÒª£ºWe study the quantitative pointwise behavior of solutions to the Boltzmann equation for hard potentials and Maxwellian molecules. A key challenge in this problem is the loss of velocity weight in linear estimates, which makes standard nonlinear iteration infeasible. To address this, we develop an Enhanced Mixture Lemma, demonstrating that mixing the transport and gain parts of the linearized collision operator can generate arbitrary-order regularity and decay in both space and velocity variables. This allows us to decompose the linearized solution into fluid (with arbitrary regularity and velocity decay) and particle (with rapid space-time decay but loss of velocity decay) components, making it possible to solve the nonlinear problem through this particle¨Cfluid duality.