论文标题
Navier-Stokes方程在半空间中具有非兼容数据
Navier-Stokes equations in the half space with non compatible data
论文作者
论文摘要
在本文中，我们将考虑具有Euler型初始条件的半平面中的Navier-Stokes方程，即在边界处具有非零切向分量的初始条件。在数据的分析假设下，我们应证明该解决方案在很小的时间内与粘度无关。该溶液是通过涉及Euler和Prandtl方程的解决方案的复合渐近扩展构建的，以及误差项。误差的标准与粘度的平方根为零。 PrandTL解决方案包含一个单数项，这会影响误差的规律性。错误项写为一阶Euler校正的总和，一阶PrandTL校正和进一步的错误项。分析设置的使用主要是由于PrandTL方程式。
In this paper we shall consider the Navier-Stokes equations in the half plane with Euler-type initial conditions, i.e. initial conditions which have a non-zero tangential component at the boundary. Under analyticity assumptions for the data, we shall prove that the solution exists for a small time independent of the viscosity. The solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, plus an error term. The norm of the error goes to zero with the square root of the viscosity. The Prandtl solution contains a singular term, which influences the regularity of the error. The error term is written as the sum of a first order Euler correction, a first order Prandtl correction, and a further error term. The use of an analytic setting is mainly due to the Prandtl equation.
