论文标题
2D HVBK方程的全球规律性
Global Regularity of the 2D HVBK equations
论文作者
论文摘要
Hall-Vinen-Bekharevich-Khalatnikov（HVBK）方程是非零温度下超流体的宏观模型。对于平滑，紧凑的支持数据，我们证明了在不可压缩的和等温的情况下，在$ \ mathbb {r}^2 $中，这些方程式强大的解决方案的全球范围很好。该证明利用收缩映射论点来建立高常规数据的局部适当性，然后在这种情况下使用Beale-Kato-Kato-Majda标准的类似物证明了全球规律性。在附录中，我们解决了2D涡度场上的足够条件，以便具有有限的动能。
The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations are a macroscopic model of superfluidity at non-zero temperatures. For smooth, compactly supported data, we prove the global well-posedness of strong solutions to these equations in $\mathbb{R}^2$, in the incompressible and isothermal case. The proof utilises a contraction mapping argument to establish local well-posedness for high-regularity data, following which we demonstrate global regularity using an analogue of the Beale-Kato-Majda criterion in this context. In the appendix, we address the sufficient conditions on a 2D vorticity field, in order to have a finite kinetic energy.
