- Tytuł:
- On the existence for the Cauchy-Neumann problem for the Stokes system in the $L_p$-framework
- Autorzy:
-
Mucha, Piotr
Zajączkowski, Wojciech - Powiązania:
- https://bibliotekanauki.pl/articles/1205939.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Stokes system
Marcinkiewicz theorem
Cauchy-Neumann initial boundary value problem
the Fourier transform
existence of solutions - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 2000, 143, 1; 75-101
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł