论文标题
用于欧拉方程的粘度解的惯性动量耗散：光滑身体周围的外流
Inertial Momentum Dissipation for Viscosity Solutions of Euler Equations: External Flow Around a Smooth Body
论文作者
论文摘要
我们研究了在存在固体边界的情况下从零粘度限制获得的不可压缩欧拉方程的弱解的局部平衡，这是一个例子，围绕有限，光滑的身体流动。我们表明，由于身体表面的分布，粘性皮肤摩擦和壁压都存在于无粘性极限中。我们为欧拉溶液定义了向壁向壁的非线性空间通量，并表明壁摩擦和压力是从该动量通量中获得的，分别是壁式距离的极限，分别为壁式和壁正态分子。我们还表明，如果速度和压力在墙壁的邻里界限，以及在壁的较小距离内消失的距离（一种精确的壁式速度速度条件形式）在壁的距离内消失，则描述异常动量转移到墙壁的皮肤摩擦将消失。在后一种情况下，所有限制阻力都是由作用在人体上的压力产生的，并且可以在欧拉溶液内部压力的壁接近内部压力的壁上时获得身体表面的压力。作为此结果的一种应用，我们表明Lighthill在墙壁上产生的涡度产生理论对于在Inviscid限制中获得的Euler溶液有效。此外，在同伴作品中，我们表明，最近用于强大的Navier-Stokes解决方案的Josephson-Anderson的关系对于在Inviscid限制中获得的弱Euler解决方案有效。
We study the local balance of momentum for weak solutions of incompressible Euler equations obtained from the zero-viscosity limit in the presence of solid boundaries, taking as an example flow around a finite, smooth body. We show that both viscous skin friction and wall pressure exist in the inviscid limit as distributions on the body surface. We define a nonlinear spatial flux of momentum toward the wall for the Euler solution, and show that wall friction and pressure are obtained from this momentum flux in the limit of vanishing distance to the wall, for the wall-parallel and wall-normal components, respectively. We show furthermore that the skin friction describing anomalous momentum transfer to the wall will vanish if velocity and pressure are bounded in a neighborhood of the wall and if also the essential supremum of wall-normal velocity within a small distance of the wall vanishes with this distance (a precise form of the vanishing wall-normal velocity condition). In the latter case, all of the limiting drag arises from pressure forces acting on the body and the pressure at the body surface can be obtained as the limit approaching the wall of the interior pressure for the Euler solution. As one application of this result, we show that Lighthill's theory of vorticity generation at the wall is valid for the Euler solutions obtained in the inviscid limit. Further, in a companion work, we show that the Josephson-Anderson relation for the drag, recently derived for strong Navier-Stokes solutions, is valid for weak Euler solutions obtained in their inviscid limit.
