On the Stationary Navier–Stokes Problem in $$\mathbb {R}^3$$ R 3 : An Approach in Weighted Sobolev Spaces

2017 ◽  
Vol 14 (3) ◽  
Author(s):  
Mondher Benjemaa ◽  
Hela Louati ◽  
Mohamed Meslameni
Keyword(s):  
Sobolev Spaces ◽  
Stokes Problem ◽  
Weighted Sobolev Spaces ◽  
Navier Stokes

THE STOKES PROBLEM IN ℝn: AN APPROACH IN WEIGHTED SOBOLEV SPACES

1999 ◽  
Vol 09 (05) ◽  
pp. 723-754 ◽  
Author(s):  
F. ALLIOT ◽  
C. AMROUCHE
Keyword(s):  
Asymptotic Expansion ◽  
Sobolev Spaces ◽  
Vector Fields ◽  
Stokes Problem ◽  
Weighted Sobolev Spaces ◽  
Explicit Representation ◽  
Solenoidal Vector ◽  
Regularity Results

We prove some existence, uniqueness and regularity results for the solutions to the Stokes problem in ℝn, n≥2 in weighted Sobolev spaces [Formula: see text]. This framework enables us to characterise for which data the problem has solutions with prescribed decay or growth at infinity. Moreover, we obtain an explicit representation as well as an asymptotic expansion of the solution for non-smooth decaying data. We also establish the density of smooth solenoidal vector fields in the subspace of [Formula: see text] such that div v=0.

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