On existence of spatially regular strong solutions for a class of transport equations

2025/04/23 by Jouko Tervo, Tervo, Jouko, Petri Kokkonen +1
Computer Science · Mathematics · #35L04 #35Q20 #35R09 #45K05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2504.16560

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

The paper considers existence of spatially regular solutions for a class of linear Boltzmann transport equations. The related transport problem is an (initial) inflow boundary value problem. This problem is characteristic with variable multiplicity, that is, the rank of the boundary matrix (here a scalar) is not constant on the boundary. It is known that for these types of (initial) boundary value problems the full higher order Sobolev regularity cannot generally be established. In this paper we present Sobolev regularity results for solutions of linear Boltzmann transport problems when the data belongs to appropriate anisotropic Sobolev spaces whose elements are zero on the inflow and characteristic parts of the boundary.

Citations

• On the sharp regularity of solutions to hyperbolic boundary value problems
• On regularity of solutions for certain linear Boltzmann transport equations
• A Revisit of the Velocity Averaging Lemma: on the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain
• On Existence of L²-solutions of Coupled Boltzmann Continuous Slowing Down Transport Equation System
• BV-regularity of the Boltzmann equation in Non-Convex Domains
• Regularity of the Boltzmann Equation in Convex Domains
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• One-parameter semigroups for linear evolution equations

Related

• On regularity of solutions for certain linear Boltzmann transport equations
• Steady transport equation in Sobolev-Slobodetskii spaces
• H^s_x regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
• Hölder regularity of solutions of the steady Boltzmann equation with soft potentials
• Regularity of stationary solutions to the linearized Boltzmann equations