论文标题
全球存在具有非平凡远场行为的量子Navier-Stokes方程的有限能量弱解决方案
Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior
论文作者
论文摘要
我们证明了在整个空间中量子Navier-Stokes方程的有限能弱解决方案在尺寸d = 2,3中具有非微不足道的条件。真空区域包括在方程式的弱公式中。我们的方法包括入侵域方法。更确切地说，通过使用合适的截断参数，我们构建了一系列近似解。能量和BD熵边界可以使截短配方中的极限通行，从而导致有限的能量弱溶液。此外，在具有退化粘度的可压缩Navier-Stokes方程的情况下，结果也有效。
We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The vacuum regions are included in the weak formulation of the equations. Our method consists in an invading domains approach. More precisely, by using a suitable truncation argument we construct a sequence of approximate solutions. The energy and the BD entropy bounds allow for the passage to the limit in the truncated formulation leading to a finite energy weak solution. Moreover, the result is also valid in the case of compressible Navier-Stokes equations with degenerate viscosity.
