Integrability propagation for a Boltzmann system describing polyatomic gas mixtures
This paper explores the $L^{p}$ Lebesgue's integrability propagation, $p\in(1,\infty]$, of a system of space homogeneous Boltzmann equations modelling a multi-component mixture of polyatomic gases based on the continuous internal energy. For typical collision kernels proposed in the literature,...
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11-05-2023
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| Abstract | This paper explores the $L^{p}$ Lebesgue's integrability propagation,
$p\in(1,\infty]$, of a system of space homogeneous Boltzmann equations
modelling a multi-component mixture of polyatomic gases based on the continuous
internal energy. For typical collision kernels proposed in the literature,
$L^p$ moment-entropy-based estimates for the collision operator gain part and a
lower bound for the loss part are performed leading to a vector valued
inequality for the collision operator and, consequently, to a differential
inequality for the vector valued solutions of the system. This allows to prove
the propagation property of the polynomially weighted $L^p$ norms associated to
the vector valued solution of the system of Boltzmann equations. The case
$p=\infty$ is found as a limit of the case $p<\infty$. |
|---|---|
| AbstractList | This paper explores the $L^{p}$ Lebesgue's integrability propagation,
$p\in(1,\infty]$, of a system of space homogeneous Boltzmann equations
modelling a multi-component mixture of polyatomic gases based on the continuous
internal energy. For typical collision kernels proposed in the literature,
$L^p$ moment-entropy-based estimates for the collision operator gain part and a
lower bound for the loss part are performed leading to a vector valued
inequality for the collision operator and, consequently, to a differential
inequality for the vector valued solutions of the system. This allows to prove
the propagation property of the polynomially weighted $L^p$ norms associated to
the vector valued solution of the system of Boltzmann equations. The case
$p=\infty$ is found as a limit of the case $p<\infty$. |
| Author | Pavić-Čolić, Milana Alonso, Ricardo |
| Author_xml | – sequence: 1 givenname: Ricardo surname: Alonso fullname: Alonso, Ricardo – sequence: 2 givenname: Milana surname: Pavić-Čolić fullname: Pavić-Čolić, Milana |
| BackLink | https://doi.org/10.48550/arXiv.2305.06749$$DView paper in arXiv |
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| Snippet | This paper explores the $L^{p}$ Lebesgue's integrability propagation,
$p\in(1,\infty]$, of a system of space homogeneous Boltzmann equations
modelling a... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Mathematical Physics Physics - Mathematical Physics |
| Title | Integrability propagation for a Boltzmann system describing polyatomic gas mixtures |
| URI | https://arxiv.org/abs/2305.06749 |
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