论文标题
在某些大数据类别中，粘弹性流体方程的强溶液
Strong Solutions of the Equations for Viscoelastic Fluids in Some Classes of Large Data
论文作者
论文摘要
我们研究了空间周期性域中不可压缩的粘弹性流体方程的全球强解决方案的存在和独特性，并表明如果给定物理参数的初始变形和速度较小，则在全球范围内存在独特的强溶液。特别是，对于大弹性系数，初始速度可能很大。本文的结果在数学上验证了弹性可以防止具有较大初始速度的强溶液的奇异性形成，因此在防止粘性流中奇异性形成的粘度起着相似的作用。此外，对于给定的初始速度扰动和剩余状态周围的零初始变形，我们发现，由于弹性系数或时间到达无穷大，（1）任何直线段$ l^0 $由剩余状态的流体粒子组成，在速度下的速度范围内将变成$ l^0 $ l^0 $ l^0 $ l^0。 （2）即使初始速度较大，也可以通过拉格朗日坐标中的线性无压运动来近似粘弹性流体的运动。此外，上述现象也可以在相应的可压缩流体情况下找到。
We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial deformation and velocity are small for the given physical parameters. In particular, the initial velocity can be large for the large elasticity coefficient. The result of this paper mathematically verifies that the elasticity can prevent the formation of singularities of strong solutions with large initial velocity, thus playing a similar role to viscosity in preventing the formation of singularities in viscous flows. Moreover, for given initial velocity perturbation and zero initial deformation around the rest state, we find, as the elasticity coefficient or time go to infinity, that (1) any straight line segment $l^0$ consisted of fluid particles in the rest state, after being bent by a velocity perturbation, will turn into a straight line segment that is parallel to $l^0$ and has the same length as $l^0$. (2) the motion of the viscoelastic fluid can be approximated by a linear pressureless motion in Lagrangian coordinates, even when the initial velocity is large. Moreover, the above mentioned phenomena can also be found in the corresponding compressible fluid case.
