Future global stability of Maxwell-Jüttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes
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2026
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| author | Strain, Robert M. Taylor, Martin Ruiz, Renato Velozo |
| author_facet | Strain, Robert M. Taylor, Martin Ruiz, Renato Velozo |
| contents | In this work we study the general relativistic massless Boltzmann equation on Friedmann-Lemaître-Robertson-Walker spacetimes with spatial topology $\mathbb{T}^3$ in the linear and decelerated expanding regimes, where the scale factor is $t^{\mathfrak{q}}$ with $\mathfrak{q}\in [0,1]$. The massless Boltzmann equation on these backgrounds admits non-stationary Maxwell-Jüttner equilibria of the form $\exp(- |t^{2\mathfrak{q}}p|)$. For $0 \leq \mathfrak{q} \leq 1$, we prove future global-in-time existence and uniqueness of small perturbations of these equilibria in the case of hard ball interaction without symmetry assumptions. For $0\leq \mathfrak{q} < 1/3$, we prove that the perturbation -- measured in a suitable $L^2_p$ based energy norm -- decays at the superpolynomial time-decay rate of $t^{-3\mathfrak{q}}\exp(-t^{1-3\mathfrak{q}})$, whereas for $1/3< \mathfrak{q} \leq 1$ we obtain the polynomial time-decay rate of $t^{-3\mathfrak{q}}$. In the borderline case $\mathfrak{q}=1/3$, we show the time-decay of $t^{-3\mathfrak{q} -c}$ with a uniform constant $c>0$. Finally, for $\frac{1}{3}< \mathfrak{q}\leq 1$, we prove future global-in-time existence and uniqueness of small perturbations of the vacuum solution on $\mathbb{T}^3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Future global stability of Maxwell-Jüttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes Strain, Robert M. Taylor, Martin Ruiz, Renato Velozo General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs In this work we study the general relativistic massless Boltzmann equation on Friedmann-Lemaître-Robertson-Walker spacetimes with spatial topology $\mathbb{T}^3$ in the linear and decelerated expanding regimes, where the scale factor is $t^{\mathfrak{q}}$ with $\mathfrak{q}\in [0,1]$. The massless Boltzmann equation on these backgrounds admits non-stationary Maxwell-Jüttner equilibria of the form $\exp(- |t^{2\mathfrak{q}}p|)$. For $0 \leq \mathfrak{q} \leq 1$, we prove future global-in-time existence and uniqueness of small perturbations of these equilibria in the case of hard ball interaction without symmetry assumptions. For $0\leq \mathfrak{q} < 1/3$, we prove that the perturbation -- measured in a suitable $L^2_p$ based energy norm -- decays at the superpolynomial time-decay rate of $t^{-3\mathfrak{q}}\exp(-t^{1-3\mathfrak{q}})$, whereas for $1/3< \mathfrak{q} \leq 1$ we obtain the polynomial time-decay rate of $t^{-3\mathfrak{q}}$. In the borderline case $\mathfrak{q}=1/3$, we show the time-decay of $t^{-3\mathfrak{q} -c}$ with a uniform constant $c>0$. Finally, for $\frac{1}{3}< \mathfrak{q}\leq 1$, we prove future global-in-time existence and uniqueness of small perturbations of the vacuum solution on $\mathbb{T}^3$. |
| title | Future global stability of Maxwell-Jüttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2606.00175 |