等温Matovich-Pearson方程的整体时间解
Global-in-time solutions for the isothermal Matovich-Pearson equations
摘要：
本文研究了描述玻璃纤维拉丝过程的Matovich-Pearson方程。这些方程可以看作是不可压缩Navier-斯托克斯方程的一维简化，包括自由边界，适用于细长玻璃纤维的拉制。我们集中讨论无表面张力的等温情况。然后，Matovich-Pearson方程表示轴向速度的椭圆型方程和流体横截面积的双曲线输运方程的非线性耦合系统。我们首先证明存在的局部解，并在构造适当的障碍函数，我们推断，流体半径始终是严格正的，局部解保持在同一个正则类。据我们所知，这是这个重要的方程组的第一个整体存在唯一性结果。
英文摘要：
In this paper we study the Matovich-Pearson equations describing the process of glass fiber drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-Stokes equations including free boundary, valid for the drawing of a long and thin glass fiber. We concentrate on the isothermal case without surface tension. Then the Matovich-Pearson equations represent a nonlinearly coupled system of an elliptic equation for the axial velocity and a hyperbolic transport equation for the fluid cross-sectional area. We first prove existence of a local solution, and, after constructing appropriate barrier functions, we deduce that the fluid radius is always strictly positive and that the local solution remains in the same regularity class. To the best of our knowledge, this is the first global existence and uniqueness result for this important system of equations.
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