Shape holomorphy of the stationary Navier--Stokes equations
We consider the stationary Stokes and Navier--Stokes equations for viscous, incompressible
flow in parameter dependent bounded domains D_T, subject to homogeneous Dirichlet
(``no-slip'') boundary conditions on ∂D_T. Here, D_T is the image of a given fixed reference
Lipschitz domain ̂\rmD⊆R^d, d∈{2,3\}, under a map T:R^d→R^d. We establish shape
holomorphy of Leray solutions which is to say, holomorphy of the map T↦(̂u_T,̂p_T),
where (̂u_T,̂p_T)∈H^1_0(̂D)^d*L^2(̂D) denotes the pullback of the corresponding …
flow in parameter dependent bounded domains D_T, subject to homogeneous Dirichlet
(``no-slip'') boundary conditions on ∂D_T. Here, D_T is the image of a given fixed reference
Lipschitz domain ̂\rmD⊆R^d, d∈{2,3\}, under a map T:R^d→R^d. We establish shape
holomorphy of Leray solutions which is to say, holomorphy of the map T↦(̂u_T,̂p_T),
where (̂u_T,̂p_T)∈H^1_0(̂D)^d*L^2(̂D) denotes the pullback of the corresponding …
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