- Title Information
- Title
- Initial Boundary Value Problem of the Boltzmann Equation
- Name:
Personal
- Name Part
- Kim, Chanwoo
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
- 2011
- Physical Description
- Extent
- vii, 191 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D. -- Brown University (2011)
- Name:
Personal
- Name Part
- Guo, Yan
- Role
- Role Term:
Text
- Director
- Name:
Personal
- Name Part
- Strauss, Walter
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Holmer, Justin
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Subject
- Topic
- partial differential equation
- Subject
- Topic
- Boltzmann equation
- Subject
- Topic
- boundary condition
- Subject
- Topic
- singularity
- Subject
- Topic
- large external potential
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/893484")
- Topic
- Differential equations, Partial
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20111003
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Abstract
- In this thesis, we study some boundary problems of the Boltzmann equation and the Boltzmann equation with the large external potential.If the gas is contained in a bounded domain or flows past a solid bodies, the Boltzmann equation must be accompanied by boundary conditions, which describe the interaction of the gas with the solid walls. The basic boundary conditions are in-flow injection, diffuse reflection, bounce-back, and specular reflection boundary conditions.First, we demonstrate that discontinuity of the Boltzmann solution is created at the non-convex part of the grazing boundary, then propagate only along the forward characteristics inside the domain before it hits on the boundary again with the in-flow injection, diffuse reflection and bounce-back boundary conditions. The main ingredient is the new regularizing effect of the gain term.Second, we prove the global well-posedness of the Boltzmann equation with the specular reflection boundary condition when the domain is the cylindrical shape. The main ingredients are introducing collision-pair map to show the transversality and developing the graph comparison method to characterize grazing velocities for the non-convex domains.If the gas particles are charged and there is background electonic potential, the Boltzmann equation is accompanied by the field term ∇χΦ⋅∇ᵥF in the equation. The global well-posedness in the presence of the large external potential is an important open problem. We use Asano's work, showing the transversality in the presence of potentials, in L<sup>p</sup> - L<sup>∞</sup> framework to resolve this problem.
- Identifier:
DOI
- 10.7301/Z0XD0ZX8
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations