Relaxation in Sobolev spaces and <inline-formula><tex-math id="M1">$ L^1 $</tex-math></inline-formula> spectral gap of the 1D dissipative Boltzmann equation with Maxwell interactions
We study the dynamic relaxation to equilibrium of the 1D dissipative Boltzmann equation with Maxwell interactions in classical $ H^s $ Sobolev spaces. In addition, we present a shrinkage analysis and decay estimates for the linearised 1D dissipative Boltzmann operator with such interactions. Based on this study, we explore the convergence in $ H^s $ and $ L^{1} $ spaces for the linear and nonlinear models. This study extends classical results found in the literature given for spaces with weak topologies.
Authors
- Ricardo Alonso (ORCID: https://orcid.org/0000-0001-9955-8343)
- Bertrand Lods (ORCID: https://orcid.org/0000-0001-8574-513X)
- Véronique Bagland
- Sebastian Throm
- José A. Cañizo (ORCID: https://orcid.org/0000-0001-7892-1174)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Collegio Carlo Alberto (IT)
- Universidad de Granada (ES)
- Université Clermont Auvergne (FR)
- University of Turin (IT)
- Umeå University (SE)
Publication Details
- Journal
- Discrete and Continuous Dynamical Systems
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/dcds.2025068
- Primary Topic
- Gas Dynamics and Kinetic Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Dipartimenti di Eccellenza
- Collegio Carlo Alberto
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Hausdorff Center for Mathematics