On the existence for the Cauchy-Neumann problem for the Stokes system in the Lp-framework
Mucha, Piotr ; Zajączkowski, Wojciech
Studia Mathematica, Tome 141 (2000), p. 75-101 / Harvested from The Polish Digital Mathematics Library
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The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain Ω⊂ℝ3 is proved in a class such that the velocity belongs to Wr2,1(Ω×(0,T)), where r > 3. The proof is divided into three steps. First, the existence of solutions is proved in a half-space for vanishing initial data by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216810 
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Mucha, Piotr; Zajączkowski, Wojciech. On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework. Studia Mathematica, Tome 141 (2000) pp. 75-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv143i1p75bwm/

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