## Departmental PhD Thesis Exam – Brian Pigott

Everyone welcome:

DEPARTMENTAL PHD THESIS EXAM
----------------------------

Friday, June 17, 2011, 3:10 p.m., in BA 6183

PhD Candidate:  Brian Pigott

Thesis title:   Low Regularity Stability for Subcritical Generalized
Korteweg-de Vries Equations

Thesis abstract:

In this thesis we prove polynomial-in-time upper bounds for the
orbital instability of solitons for subcritical generalized
Korteweg-de Vries equations in $H^{s}_{x}(\R)$ with $s < 1$.
By combining coercivity estimates of Weinstein with the $I$-method
as developed by Colliander, Keel, Staffilani, Takaoka, and Tao,
we construct a modified energy functional which is shown to be
almost conserved while providing us with an estimate of the
deviation of the solution from the ground state curve. The iteration
of the almost conservation law for the modified energy functional
over time intervals of uniform length yields the polynomial upper
bound.

A copy of the thesis can be obtained by contacting
bpigott@math.toronto.edu.

Refreshments will be served in the Math Lounge before the exam.