194 research outputs found
On the Navier problem for the stationary Navier–Stokes equations
No full textAbstractThe Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity. We prove that a solution exists in a bounded domain provided ‖a‖L2(∂Ω) is less than a computable positive constant and is unique if ‖a‖W1/2,2(∂Ω)+‖s‖L2(∂Ω) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ‖a‖L2(∂Ω)+‖a−u0⋅n‖L2(∂Ω) is small
On the Asymptotic Behaviour of the Solutions of the Equations of Linear Elastodynamics in Unbounded Domains
No full textStrong uniqueness theorems and the Phragmen-Lindelof principle in nonhomogeneous elastostatics
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Some properties of the solutions of the equations of linear elastodynamics in unbounded domains
No full textOn the Stokes problem with data in L1
No full textWe consider the steady Stokes equations in bounded and exterior domains Ω of R3 with boundary data and forces in L1. We prove existence and uniqueness of a weak solution with gradient in the Iwaniek–Sbordone grand Lebesgue space 3) L3/2)
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