论文标题
适合粘度的非均匀不可压缩流体的适应性理论
Well-posedness theory for non-homogeneous incompressible fluids with odd viscosity
论文作者
论文摘要
几种流体系统的特征是时间逆转和平等破裂。这种现象的例子在量子和经典的流体动力学中出现。在这些情况下，粘度张量通常被称为``奇粘度''，变得无疾病。在数学层面上，这一事实转化为\ textsl {a先验}估计的衍生物的损失：虽然奇数粘度项取决于速度场的衍生物，但无法预期抛物线平滑效果。 在本文中，我们在Sobolev空间中建立了一个良好的度理论，用于具有奇特粘度的不可压缩的非均匀流体系统。分析的关键点是引入一组\ emph {良好的未知数}，它允许将方程式系统的隐藏双曲线结构出现出来。正是这种双曲结构使得可以规避衍生物损失并传播溶液的足够高的Sobolev规范。适当的结果是局部的。还建立了两个延续标准。
Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed ``odd viscosity'', becomes non-dissipative. At the mathematical level, this fact translates into a loss of derivatives at the level of \textsl{a priori} estimates: while the odd viscosity term depends on derivatives of the velocity field, no parabolic smoothing effect can be expected. In the present paper, we establish a well-posedness theory in Sobolev spaces for a system of incompressible non-homogeneous fluids with odd viscosity. The crucial point of the analysis is the introduction of a set of \emph{good unknowns}, which allow for the emerging of a hidden hyperbolic structure underlying the system of equations. It is exactly this hyperbolic structure which makes it possible to circumvent the derivative loss and propagate high enough Sobolev norms of the solution. The well-posedness result is local in time; two continuation criteria are also established.
