Geodesic
On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework
Studia Mathematica, Tome 143 (2000) no. 1, pp. 75-101

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The existence for the Cauchy-Neumann problem for the Stokes system in a bounded domain $Ω ⊂ ℝ^3$ is proved in a class such that the velocity belongs to $W^{2,1}_r (Ω × (0,T))$, 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.
DOI : 10.4064/sm-143-1-75-101
Keywords: Stokes system, Marcinkiewicz theorem, Cauchy-Neumann initial boundary value problem, the Fourier transform, existence of solutions

Piotr Mucha 1 ; Wojciech Zajączkowski 1

1 
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Piotr Mucha; Wojciech Zajączkowski. On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework. Studia Mathematica, Tome 143 (2000) no. 1, pp. 75-101. doi: 10.4064/sm-143-1-75-101

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