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带最大密度限制的Navier-Stokes方程的耗散测度值解
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Abstract:
本文研究具有最大密度限制的可压Navier-Stokes方程，其中，最大密度限制是由一个奇性的压强项给定的。利用带有参数K的Brenner模型，我们构造了Navier-Stokes方程的逼近解。为了处理压强的奇性，引入一个逼近压强pθ,δ，其中θ,δ为逼近参数。当这些参数K,θ,δ→0时，我们证明逼近解收敛到Navier- Stokes方程的耗散测度值解。
This paper considers the compressible Navier-Stokes equation with maximum density constraint, where the maximum density constraint is imposed by a singular pressure term. Approximate solu-tions of the Navier-Stokes equation are constructed using the Brenner model with a parameter K. To deal with the singularity of pressure, an approximate pressure pθ,δ is introduced, where θ,δ are the approximate parameters. When K,θ,δ→0 , we show that the approximate solutions con-verge to the dissipative measure-valued solution of the Navier-Stokes equation.
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