PDE seminar: Motion of the inviscid gas through a nozzle -existence of a time global solution and invariantregions-

2013-7-8 16:30 - 2013-7-8 17:30
Faculty of Science Building #3, Room 309
Naoki Tsuge (Faculty of Education, Gifu Univ.)
We are concerned with the motion of the gas through
a nozzle. The phenomena are governed by the compressible
Euler equations. First, we review how the
nozzle flow is applied in physics and engineering.
Moreover, we refer to the relation between the nozzle
flow and the solar wind, which is caused by an aurora.
Next, we consider the existence of a time global solution
for the present problem. We survey the relative
results and the main theorem in this talk. Finally, we
study the bounded estimate of solutions, which is the
most difficult point to prove the time global existence.
Then, invariant regions play an important role. In this
talk, to solve our problem, we introduce an invariant
region depending on a space variable.