Date of Award
Master of Science (MS)
Gnana Bhaskar Tenali
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.
Solomon, Caleb, "Global Upper Bounds for The Landau Equation of Plasma Physics in The Very Soft Potentials Case" (2023). Theses and Dissertations. 1259.