More Like this

1. Global Hilbert Expansion for the Relativistic Vlasov–Maxwell–Boltzmann System

   https://doi.org/10.1007/s00220-021-04079-x  

   Guo, Yan and (September 2021, Communications in mathematical physics)

   Consider the relativistic Vlasov–Maxwell–Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works Germain and Masmoudi (Ann Sci Éc Norm Supér 47(3):469–503, 2014), Guo et al. (J Math Phys 55(12):123102, 2014) and Deng et al. (Arch Ration Mech Anal 225(2):771–871, 2017), we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler–Maxwell system as the mean free path goes to zero. Our method is based on the L2 − L∞ framework and the Glassey–Strauss Representation of the electromagnetic field, with auxiliary H1 estimates and W1,∞ estimates to control the characteristic curves and corresponding L∞ norm. 

   more » « less
2. A toy model for the relativistic Vlasov-Maxwell system

   https://doi.org/10.3934/krm.2021053  

   Ben-Artzi, Jonathan; Pankavich, Stephen; Zhang, Junyong (January 2022, Kinetic and Related Models)

   The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified "toy model" is presented and studied. This toy model retains one crucial aspect of the RVM system: the phase-space evolution of the distribution function is governed by a transport equation whose forcing term satisfies a wave equation with finite speed of propagation. 

   more » « less
3. Kinetic description of stable white dwarfs

   https://doi.org/10.3934/krm.2021033  

   Jang, Juhi; Seok, Jinmyoung (January 2022, Kinetic and Related Models)

   In this paper, we study fermion ground states of the relativistic Vlasov-Poisson system arising in the semiclassical limit from relativistic quantum theory of white dwarfs. We show that fermion ground states of the three dimensional relativistic Vlasov-Poisson system exist for subcritical mass, the mass density of such fermion ground states satisfies the Chandrasekhar equation for white dwarfs, and that they are orbitally stable as long as solutions exist. 

   more » « less
4. Global existence for an isotropic modification of the Boltzmann equation

   https://doi.org/10.1016/j.jfa.2024.110423  

   Snelson, Stanley (June 2024, Journal of Functional Analysis)

   Motivated by the open problem of large-data global existence for the non-cutoff Boltzmann equation, we introduce a model equation that in some sense disregards the anisotropy of the Boltzmann collision kernel. We refer to this model equation as isotropic Boltzmann by analogy with the isotropic Landau equation introduced by Krieger and Strain (2012) [35]. The collision operator of our isotropic Boltzmann model converges to the isotropic Landau collision operator under a scaling limit that is analogous to the grazing collisions limit connecting (true) Boltzmann with (true) Landau. Our main result is global existence for the isotropic Boltzmann equation in the space homogeneous case, for certain parts of the “very soft potentials” regime in which global existence is unknown for the space homogeneous Boltzmann equation. The proof strategy is inspired by the work of Gualdani and Guillen (2022) [22] on isotropic Landau, and makes use of recent progress on weighted fractional Hardy inequalities. 

   more » « less
5. Real‐Time Functional Assay of Volumetric Muscle Loss Injured Mouse Masseter Muscles via Nanomembrane Electronics

   https://doi.org/10.1002/advs.202101037  

   Kim, Hojoong; Kwon, Young‐Tae; Zhu, Carol; Wu, Fang; Kwon, Shinjae; Yeo, Woon‐Hong; Choo, Hyojung J. (July 2021, Advanced Science)

   Abstract Skeletal muscle has a remarkable regeneration capacity to recover its structure and function after injury, except for the traumatic loss of critical muscle volume, called volumetric muscle loss (VML). Although many extremity VML models have been conducted, craniofacial VML has not been well‐studied due to unavailable in vivo assay tools. Here, this paper reports a wireless, noninvasive nanomembrane system that integrates skin‐wearable printed sensors and electronics for real‐time, continuous monitoring of VML on craniofacial muscles. The craniofacial VML model, using biopsy punch‐induced masseter muscle injury, shows impaired muscle regeneration. To measure the electrophysiology of small and round masseter muscles of active mice during mastication, a wearable nanomembrane system with stretchable graphene sensors that can be laminated to the skin over target muscles is utilized. The noninvasive system provides highly sensitive electromyogram detection on masseter muscles with or without VML injury. Furthermore, it is demonstrated that the wireless sensor can monitor the recovery after transplantation surgery for craniofacial VML. Overall, the presented study shows the enormous potential of the masseter muscle VML injury model and wearable assay tool for the mechanism study and the therapeutic development of craniofacial VML. 

   more » « less