Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 118, pp. 128.
Stability of energycritical nonlinear Schrodinger
equations in high dimensions
Terence Tao, Monica Visan
Abstract:
We develop the existence, uniqueness, continuity, stability,
and scattering theory for energycritical nonlinear Schrodinger
equations in dimensions
,
for solutions which have large,
but finite, energy and large, but finite, Strichartz norms.
For dimensions
,
this theory is a standard extension
of the small data wellposedness theory based on iteration in
Strichartz spaces. However, in dimensions
there is an
obstruction to this approach because of the subquadratic nature
of the nonlinearity (which makes the derivative of the nonlinearity
nonLipschitz). We resolve this by iterating in exotic Strichartz
spaces instead. The theory developed here will be applied in a
subsequent paper of the second author, [21],
to establish global wellposedness and scattering for the
defocusing energycritical equation for large energy data.
Submitted July 2, 2005. Published October 26, 2005.
Math Subject Classifications: 35J10.
Key Words: Local wellposedness; uniform wellposedness; scattering theory;
Strichartz estimates
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Terence Tao
Department of Mathematics
University of California
Los Angeles, CA 900951555, USA
email: tao@math.ucla.edu 

Monica Visan
Department of Mathematics
University of California
Los Angeles, CA 900951555, USA
email: mvisan@math.ucla.edu 
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