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On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework

100%

Mucha P. B., Zajączkowski W.

Studia Mathematica

2000

tom 143

nr 1

75-101

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.

Ograniczanie wyników

1 Studia Mathematica

1 Mucha P. B.

1 Zajączkowski W.

1 2000

Wyniki wyszukiwania

On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework