论文标题
不可压缩的流体方程解决方案的能源保护：Hölder案例和与Onsager的猜想的连接
Energy conservation for weak solutions of incompressible fluid equations: the Hölder case and connections with Onsager's conjecture
论文作者
论文摘要
在本文中，我们为霍尔德连续函数类别的Euler和Navier-Stokes方程较弱的解决方案提供了基本的节能证明，放宽了有关时间变量的某些假设（在初始时间的集成性和规律性），并以统一的方式呈现它们。然后，在最后一部分中，我们证明（对于Navier-Stokes方程）是在存在固体边界和具有Dirichlet边界条件的情况下节能的结果。在粘性的情况下，这个结果似乎是Hölder类型假设的第一个结果，但没有对压力的其他假设。
In this paper we give elementary proofs of energy conservation for weak solutions to the Euler and Navier-Stokes equations in the class of Hölder continuous functions, relaxing some of the assumptions on the time variable (both integrability and regularity at initial time) and presenting them in a unified way. Then, in the final section we prove (for the Navier-Stokes equations) a result of energy conservation in presence of a solid boundary and with Dirichlet boundary conditions. This result seems the first one -- in the viscous case -- with Hölder type assumptions, but without additional assumptions on the pressure.
