GREAT PROBLEMS IN NONLINEAR EVOLUTION EQUATIONS <>
This
is another philosophical lecture delivered at the AMS Millenium Conference in Los Angeles, August, 2000.
PDE
AS A UNIFIED SUBJECT <>
This
is a philosophical essay reflecting my personal views about PDE's. To appear
in the proceedings of the conference `` Visions in Mathematics'' Tel Aviv
1999.
A
COMMUTING VECTORFIELD APPROACH TO STRICHARTZ TYPE INEQUALITIES AND APPLICATIONS
TO QUASILINEAR WAVE EQUATIONS
This
paper marks my whole- hearted return to quasilinear wave equations, after
a detour of more than ten years. I show that one can recover some of the
recent results of Chemin-Bahouri and Tataru by reducing the crucial dispersive
inequality( the key ingredient in the Strichartz type estimates) to L^2--L^\infty
decay estimates based on energy estimates and an adaptation of the commuting
vectorfields method.
Some
General Remarks on Nonlinear PDEs
Geometric
and Fourier Methods in Nonlinear Wave Equations)
(Lecture
in Tel-Aviv, Aug, 1999)
Bilinear
Estimates and Applications to Nonlinear Wave Equations
This
is a survey paper in collaboration with S. Selberg concerning optimal
well posedness
results
for nonlinear wave equations such as Wave Maps, Maxwell-Klein-Gordon and
Yang
Mills. The survey provides a unified treatment and simplified proofs
for some old results of Klainerman-Machedon, Klainerman-Selberg,
Klainerman-Tataru.