300 research outputs found
An Improvement on the Br\'ezis-Gallou\"et technique for 2D NLS and 1D half-wave equation
We revise the classical approach by Br\'ezis-Gallou\"et to prove global well
posedness for nonlinear evolution equations. In particular we prove global
well--posedness for the quartic NLS posed on general domains in
with initial data in , and for the quartic
nonlinear half-wave equation on with initial data in
Blow-up for self-interacting fractional Ginzburg-Landau equation
The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau
equation with non-positive nonlinearity is shown by an ODE argument. Moreover,
in one dimensional case, the optimal lifespan estimate for size of initial data
is obtained.Comment: 8 pages, no figure
- …