A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in W−1/q,q

103 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Existence and Regularity of Very Weak Solutions of the Stationary Navier–Stokes Equations (2009, methodology): “On the other hand, the notion of very weak solutions has been introduced by Giga [12], Conca [3], Galdi et al. [ 9 ] and Farwig et al. [4,5] to prove unique solvability of the Stokes equations with very irregular boundary data, that is, boundary data in L q (∂Ω) or more generally in W −1/q,q (∂Ω).”
State-constrained optimal control of the three-dimensional stationary Navier–Stokes equations☆ (2008, unknown): “In the fluid mechanics context, this type of solutions have been considered in [16] for problems with boundary data in spaces of low regularity.”
Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data (2011, background): “Observe that in [21] Theorem 3, the domain considered is of class C2,1 instead of class C1,1, and the divergence term h ∈ L p( ) instead of h ∈ Lr ( ).”
A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data (2006, background): “To prove uniqueness we follow [ 15 ] and assume that there exists another very weak solution v ∈ L q () of the system (1.8) with the same data F, k, g as for u. Setting U = u − v we can show that the equation h U, ¢w + v ¢ ∇ w + u ¢ (∇w) T + kwi = 0 (3.24)”