We consider the abstract initial value problem for the system of evolution equations which describe motion of incompressible viscous and heat-conductive fluids in a bounded domain.
It is difficulty of our problem that we do not neglect the viscous dissipation function in contrast to the Boussinesq approximation.
This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data.
Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data.
We prove the above properties by the theory of analytic semigroups on Banach spaces.
Publié le : 2010-11-15
Classification:
Incompressible viscous and heat-conductive fluids,
abstract initial value problem,
analytic semigroups on Banach spaces,
35Q35,
35K90,
76D03
@article{1291818851,
author = {Kakizawa, Ry\^ohei},
title = {The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces},
journal = {Hiroshima Math. J.},
volume = {40},
number = {1},
year = {2010},
pages = { 371-402},
language = {en},
url = {http://dml.mathdoc.fr/item/1291818851}
}
Kakizawa, Ryôhei. The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces. Hiroshima Math. J., Tome 40 (2010) no. 1, pp. 371-402. http://gdmltest.u-ga.fr/item/1291818851/