Everyone welcome:


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

PhD Candidate:  Brian Pigott

PhD Advisor:    James Colliander

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 

A copy of the thesis can be obtained by contacting 

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

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