Inviscid limit for Navier–Stokes equations in domains with permeable boundaries

This work is concerned with 2D-Navier Stokes equations in a multiply-connected bounded domain with permeable walls. The permeability is described by a Navier type condition. Our aim is to show that the inviscid limit is a solution of the Euler equations, satisfying the Navier type condition on the inflow zone of the walls.     

Weak Continuity and Compactness for Nonlinear Partial Differential Equations

This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.     

Euler–Goursat-like formula via Laplace–Borel duality

The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities.     

AN ITERATION METHOD FOR INCOMPRESSIBLEVISCOUS/INVISCID COUPLED PROBLEM VIA A SPECTRALAPPROXIMATION

1.IntroductionDomaindecompositionmethodsareusefulapproximationtechniquestofacecomputationalfluiddynamicsproblems,especiallyincomplexphysicaldomainsandusingparallelcomputationalenvironments.Theyhavebeenfirstemployedinfinitedifferenceandfiniteelementme...     

Coupled fluid–solid interaction under shock wave loading

This paper considers the treatment of fluid–solid interaction problems under shock wave loading, where the solid experiences large bulk Lagrangian displacements. This work addresses the issues associated with using a level set as a generalized interface for fluid–solid coupling where the fluid–solid interface is embedded in an unstructured fluid grid. We outline the formulation used for the edge‐based unstructured‐grid Euler solver. The identification of the fluid–solid interface on the unstructured fluid mesh uses a super‐sampled ??² projection technique, which in conjunction with a Lagrangian interface position, permits fast identification of the interface and the concomitant imposition of boundary conditions. The use of a narrow‐band approach for the identification of the wetted interface is presented with the details of the construction of interface conditions. A series of two and three‐dimensional shock‐body computations are presented to demonstrate the validity of the current approach on problems with static and dynamic interfaces, including projectile/shock interaction simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

The optimal upper bound of the number of generalized Euler configurations

Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two masses and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper bound of the number of generalized Euler configurations for the cases b 1 and b = 2, 3. This paper obtains the optimal upper bound for the remaining real values of b in a systematic way.     

Parametric Euler sum identities

We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums.     

与Euler函数有关的误差项均值估计

设ψ(n)是Euler函数,r是正实数.以E(x,r)表示和式的渐近公式中的误差项,本文研究了E(x,r)的算术均值和积分均值.     

Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation

Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of the PVI equation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 252–264, May, 2008.     

Well-posedness of the free-surface incompressible Euler equations with or without surface tension

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.