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摘要:
In this paper we consider the initial value problem to the fractional compressible isentropic generalized Navier-Stokes equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations is described by the nonlocal fractional Laplace operator. We give one detailed spectrum analysis on a linearized operator and the decay law in time of the solution semigroup for the linearized fractional compressible isentropic generalized Navier-Stokes equations around a constant state by the Fourier analysis technique, which is shown that the order of the fractional derivatives plays a key role in the analysis so that the spectrum structure involved here is more complex than that of the classical compressible Navier-Stokes system. Based on this and the elaborate energy method, the global-in-time existence and one optimal decay rate in time of the smooth solution are obtained under the assumption that the initial data are given in a small neighborhood of a constant state. (c) 2023 Elsevier Inc. All rights reserved.
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通讯作者信息:
来源 :
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN: 0022-0396
年份: 2023
卷: 377
页码: 369-417
2 . 4 0 0
JCR@2022
ESI学科: MATHEMATICS;
ESI高被引阀值:9
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