Wednesday, November 15, 2023 - 16:00 in U2-232
Global wellposedness of general evolution PDE on the Fourier half space
A talk in the Oberseminar Analysis series by
Kenji Nakanishi from RIMS Kyoto
| Abstract: |
This is joint work with Baoxiang Wang (Jimei and Peking). We
study the Cauchy problem for general nonlinear PDEs on the Euclidean
space given by Fourier multipliers and analytic nonlinearity. Examples
of PDE include various nonlinear hyperbolic, parabolic and dispersive
equations, the Navier-Stokes and the Euler equations, as well as the
backward heat equations and more strange ones. Restricting the Fourier
support of initial data to the half space, we prove the global
wellposendess with no size restriction in a function space of
distributions for the Fourier transform. The initial data have to be
complex valued, but may be very rough, grow polynomially at infinity,
and contain mixture of periodic functions. The global wellposedness
holds even when the solutions blow up in the classical sense.
Within the CRC this talk is associated to the project(s): A1 |
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