346 research outputs found
On Blow-up criterion for the Nonlinear Schr\"{o}dinger Equation
The blowup is studied for the nonlinear Schr\"{o}dinger equation
with is odd and (the
energy-critical or energy-supercritical case). It is shown that the solution
with negative energy blows up in finite or infinite time. A new
proof is also presented for the previous result in \cite{HoRo2}, in which a
similar result but more general in a case of energy-subcritical was shown.Comment: In this version, we add a reference, and change some expressions in
Englis
Subsonic steady-states for bipolar hydrodynamic model for semiconductors
In this paper, we study the well-posedness, ill-posedness and uniqueness of
the stationary 3-D radial solution to the bipolar isothermal hydrodynamic model
for semiconductors. The density of electron is imposed with sonic boundary and
interiorly subsonic case and the density of hole is fully subsonic case
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