On existence of solutions for the nonstationary Stokes system with boundary slip conditions

Wisam Alame

Applicationes Mathematicae (2005)

  • Volume: 32, Issue: 2, page 195-223
  • ISSN: 1233-7234

Abstract

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Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to W p 2 , 1 ( Ω × ( 0 , T ) ) , and pressure belongs to W p 1 , 0 ( Ω × ( 0 , T ) ) for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space 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.

How to cite

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Wisam Alame. "On existence of solutions for the nonstationary Stokes system with boundary slip conditions." Applicationes Mathematicae 32.2 (2005): 195-223. <http://eudml.org/doc/278996>.

@article{WisamAlame2005,
abstract = {Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to $W_p^\{2,1\}(Ω × (0,T))$, and pressure belongs to $W_p^\{1,0\}(Ω × (0,T))$ for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space 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.},
author = {Wisam Alame},
journal = {Applicationes Mathematicae},
keywords = {regularizer; Marcinkiewicz theorem on multipliers; existence of weak solutions},
language = {eng},
number = {2},
pages = {195-223},
title = {On existence of solutions for the nonstationary Stokes system with boundary slip conditions},
url = {http://eudml.org/doc/278996},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Wisam Alame
TI - On existence of solutions for the nonstationary Stokes system with boundary slip conditions
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 2
SP - 195
EP - 223
AB - Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to $W_p^{2,1}(Ω × (0,T))$, and pressure belongs to $W_p^{1,0}(Ω × (0,T))$ for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space 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.
LA - eng
KW - regularizer; Marcinkiewicz theorem on multipliers; existence of weak solutions
UR - http://eudml.org/doc/278996
ER -

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