Global classical solutions to the relativistic Boltzmann equation without angular cut-off / Jang, Jin Woo.

Format:

Book

Thesis/Dissertation

Author/Creator:

Jang, Jin Woo, author.

Contributor:

Strain, Robert M., degree supervisor.

Kadison, Richard V., 1925- degree committee member.

Gressman, Philip T., 1978- degree committee member.

University of Pennsylvania. Mathematics, degree granting institution.

Language:

English

Subjects (All):

Mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Local Subjects:

Mathematics.

Mathematics--Penn dissertations.

Penn dissertations--Mathematics.

Genre:

Academic theses.

Physical Description:

1 online resource (135 pages)

Contained In:

Dissertation Abstracts International 77-11B(E).

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2016.

Language Note:

English

System Details:

Mode of access: World Wide Web.

text file

Summary:

We prove the unique existence and exponential decay of global in time classical solutions to the special relativistic Boltzmann equation without any angular cut-off assumptions with initial perturbations in some weighted Sobolev spaces. We consider perturbations of the relativistic Maxwellian equilibrium states. We work in the case of a spatially periodic box. We consider the general conditions on the collision kernel from Dudynski and Ekiel-Jezewska (Commun. Math. Phys. 115(4):607-629,1985). Additionally, we prove sharp constructive upper and coercive lower bounds for the linearized relativistic Boltzmann collision operator in terms of a geometric fractional Sobolev norm; this shows that a spectral gap exists and that this behavior is similar to that of the non-relativistic case as shown by Gressman and Strain (Journal of AMS 24(3), 771-847, 2011). We also derive the relativistic analogue of Carleman dual representation of Boltzmann collision operator. Lastly, we explicitly compute the Jacobian of a collision map (p, q) → (thetap' + (1 -- theta) p, q) for a fixed theta ∈ (0, 1), and it is shown that the Jacobian is bounded above in p and q. This is the first global existence and stability result for relativistic Boltzmann equation without angular cutoff and this resolves the open question of perturbative global existence for the relativistic kinetic theory without the Grad's angular cut-off assumption.

Notes:

Source: Dissertation Abstracts International, Volume: 77-11(E), Section: B.

Advisors: Robert M. Strain; Committee members: Philip T. Gressman; Richard V. Kadison.

Department: Mathematics.

Ph.D. University of Pennsylvania 2016.

Local Notes:

School code: 0175

ISBN:

9781339928678

Access Restriction:

Restricted for use by site license.