研究了一类带有非局部效应的流体模型.这类模型由可压缩Euler方程和不可压缩Navier-Stokes方程耦合构成,其中非局部项的通信核具有分数阶Laplacian算子结构.将Euler方程组等效重构为具有对称结构的双曲系统,在克服非局部项带来的非线性性质后,应用能量估计的方法,建立了此类模型初值问题的局部适定性理论和正则性准则.
This paper studied a class of fluid models with non-local effects, which consisted of compressible Euler equations coupled with incompressible Navier-Stokes equations, where the communication kernel of the non-local terms had a fractional Laplacian operator structure. Euler equations were reconstructed into a hyperbolic system with symmetric structure. After overcoming the nonlinear properties of non-local terms, the local well-posedness theory and regularity criterion were established for the initial value problems of such models by using the method of energy estimation.
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