Date of Award

5-2023

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Advisor

Stanley Snelson

Second Advisor

Chelakara Subramanian

Third Advisor

Kanishka Perera

Fourth Advisor

Gnana Bhaskar Tenali

Abstract

This paper explores global upper bounds for solutions of the Landau equation in the soft potentials case (γ < −2). In particular, this paper explores the case of γ ∈ [−3,−2). Working with a classical solution to the Landau equation weighted by a cut-off function χ and using the Moser iteration, an upper bound for the L∞v norm of the solution to the Landau equation f is obtained proportianally to the L2 v norm of f with the assumptions of positive, essentially bounded coefficients. The supremum of f for t ∈ [0, T], x ∈ R3, v ∈ BR for some large radius R is shown to be bounded polynomially in R.

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