The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces
Kakizawa, Ryôhei
Hiroshima Math. J., Tome 40 (2010) no. 1, p. 371-402 / Harvested from Project Euclid
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/