Consider a two-dimensional laminar flow between two plates, so that $$(x_1,x_2)\in {{\mathbb {R}}}\times [-1,1]$$ , given by $${{\mathbf {v}}}(x_1,x_2)=(U(x_2),0)$$ where $$U\in C^4([-1,1])$$ satisfies $$U^\prime \ne 0$$ in $$[-1,1]$$ . We prove the is linearly stable large Reynolds number limit, different cases: assume either no-slip or fixed traction force (Navier-slip) conditions on and an a...

In this paper, we study the transition threshold problem for 2-D Navier-Stokes equations around Poiseuille flow (1?y2,0) in a finite channel with Navier-slip boundary condition. Based on resolvent estimates linearized operator flow, first establish enhanced dissipation sharp decay rate e?c?t. As an application, prove that if initial perturbation of vorticity satisfies??0?L2?c0?34 some small con...

In this paper we study a class of quasi-variational-hemivariational inequalities in reflexive Banach spaces. The contain convex potential, locally Lipschitz superpotential, and implicit obstacle set constraints. Solution existence compactness the solution to inequality problem are established based on Kakutani–Ky Fan fixed point theorem. applicability results is illustrated by steady-state Osee...

We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is coupled between Navier-Stokes equation for fluid velocity transported heat harmonic maps, and both these parabolic equations are critical analysis in two dimensions. The conditions physically natural they correspond to Navier slip condition zero friction field...

Micropolar fluids are with microstructure and belong to a class of asymmetric stress tensor that called Polar fluids, include, as special case, the well-established Navier–Stokes model. In this work we study 3D micropolar model Navier boundary conditions without friction for velocity field homogeneous Dirichlet angular velocity. Using Galerkin method, prove existence weak solutions establish Pr...