2022/01/05 by Gi-Chan Bae, Bae, Gi-Chan, Christian Klingenberg +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2201.01611
openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \citemixmodel when the initial data is a small perturbation of global equilibrium. For this, we carefully analyze the dissipative nature of the linearized multi-component relaxation operator, and observe that the partial dissipation from the intra-species and the inter-species linearized relaxation operators are combined in a complementary manner to give rise to the desired dissipation estimate of the model We also observe that the convergence rate of the distribution function increases as the momentum-energy interchange rate between the different components of the gas increases.