Concerning the W k,p -Inviscid Limit for 3-D Flows Under a Slip Boundary Condition

We consider the 3-D evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, see (1.2), and study the problem of the strong convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We prove here, in the flat boundary case, convergence in Sobolev spaces W ^k, p (Ω), for arbitrarily large k and p (for previous results see Xiao and Xin in Comm Pure Appl Math 60:1027–1055, 2007 and Beir?o da Veiga and Crispo in J Math Fluid Mech, 2009, doi:). However this problem is still open for non-flat, arbitrarily smooth, boundaries. The main obstacle consists in some boundary integrals, which vanish on flat portions of the boundary. However, if we drop the convective terms (Stokes problem), the inviscid, strong limit result holds, as shown below. The cause of this different behavior is quite subtle. As a by-product, we set up a very elementary approach to the regularity theory, in L ^p -spaces, for solutions to the Navier–Stokes equations under slip type boundary conditions.     

Sharp Inviscid Limit Results under Navier Type Boundary Conditions. An L p Theory

We consider the evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, and study the convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We obtain quite sharp results in the 2-D and 3-D cases. However, in the 3-D case, we need to assume that the boundary is flat.     

Higher Integrability of Solutions to Generalized Stokes System Under Perfect Slip Boundary Conditions

We prove an L ^q theory result for generalized Stokes system in a \({\mathcal{C}^{2,1}}\) domain complemented with the perfect slip boundary conditions and under Φ-growth conditions. Since the interior regularity was obtained in Diening and Kaplický (Manu Math 141:336–361, 2013), a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderón–Zygmund theory and the method developed in Caffarelli and Peral (Ann Math 130:189–213, 1989). We obtain higher integrability of the first gradient of a solution.     

The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness

We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference velocities (u ₀, v ₀) and reference height ${\phi_0}$ (sub- or super-critical flow at each part of the boundary).     

外边界支承环板在局部线性分布荷载作用下的塑性极限分析

针对外边界支承的团支和简支环板，应用广义阶梯函数给出了环板在局部线性分布荷载作用下的极限荷载的计算公式。     

A 2.5-D dynamic model for a saturated porous medium. Part II: Boundary element method

The 3-D boundary integral equation is derived in terms of the reciprocal work theorem and used along with the 2.5-D Green’s function developed in Part I [Lu, J.F., Jeng, D.S., Williams, S., submitted for publication. A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function. Int. J. Solids Struct.] to develop the 2.5-D boundary integral equation for a saturated porous medium. The 2.5-D boundary integral equations for the wave scattering problem and the moving load problem are established. The Cauchy type singularity of the 2.5-D boundary integral equation is eliminated through introduction of an auxiliary problem and the treatment of the weakly singular kernel is also addressed. Discretisation of the 2.5-D boundary integral equation is achieved using boundary iso-parametric elements. The discrete wavenumber domain solution is obtained via the 2.5-D boundary element method, and the space domain solution is recovered using the inverse Fourier transform. To validate the new methodology, numerical results of this paper are compared with those obtained using an analytical approach; also, some numerical results and corresponding analysis are presented.     

Calculation of all drag components for 3-D bodies in wind tunnel flows. A boundary element-wake approach

A boundary element-wake numerical approach is developed and used to determine all drag components of a three dimensional body in a wind tunnel flow. The approach decomposes the total drag into three components; the profile drag, the cross flow drag (induced drag), and the tunnel-wall effect component, each with its own physical significance. Additionally, the cross flow drag component is divided into two components, the vortex component and the source (dilatation) component. In the present approach, the transverse kinematics relations are expressed as integral representations of the axial vorticity and the transverse dilatation (source strength). This advantage permits the vortex and the source drag computations to be performed only in the vortical area of the transverse wake and hence avoids excessive computations. Also, the procedures distinguish the contribution of the transverse dilatation to the cross flow drag. The validity of the present procedure is examined by comparing the present results against the experimental data of reference [1] for a car and wing models. The comparison shows that the present computed total drag, for the wing and the car models, agrees very well with the experimental data, provided that the wake data are measured at survey planes moderately distant from the body.