论文标题
与Navier Stokes方程相互作用的弹性板的弱唯一性
Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation
论文作者
论文摘要
我们显示了由Navier-Stokes方程与柔性的弹性板相互作用的两位或三维流体运动的弱唯一性和稳定性结果。该板位于流体的顶部，因此决定了含有流体的时间变化域的可变部分（因此是溶液的一部分）。唯一性结果是稳定性估计值的结果，在这种估计中，两种溶液的差异是通过初始值和外部力的距离估算的。为此，我们介绍了一种方法，该方法克服了流体速度和压力的两个（时间变量）域的问题。估计值是在两个弱解决方案之一具有较高的规律性的假设下。在给定的框架中，要求额外的规律性仅要求类似于著名的Ladyzhenskaya-serrodi-serrin条件的解决方案的速度。
We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the given framework.
