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Bae, Hantaek
School of Natural Science
Research Interests
  • Fluid dynamics, polymeric fluid, kinetic theory

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Analyticity of solutions to the barotropic compressible Navier-Stokes equations

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Title
Analyticity of solutions to the barotropic compressible Navier-Stokes equations
Author
Bae, Hantaek
Issue Date
2020-07
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.269, no.2, pp.1718 - 1743
Abstract
In this paper, we establish analyticity of solutions to the barotropic compressible Navier-Stokes equations describing the motion of the density rho and the velocity field u in R-3. We assume that rho(0) is a small perturbation of 1 and (1 - 1/rho(0), u(0)) are analytic in Besov spaces with analyticity radius omega > 0. We show that the corresponding solutions are analytic globally in time when (1 - 1/rho(0), u(0)) are sufficiently small. To do this, we introduce the exponential operator e((omega-theta(t))D) acting on (1 - 1/rho, u), where D is the differential operator whose Fourier symbol is given by vertical bar xi vertical bar(1)=vertical bar xi(1)vertical bar + vertical bar xi(2)vertical bar + vertical bar xi(3)vertical bar and theta(t) is chosen to satisfy theta(t) < omega globally in time. (C) 2020 Elsevier Inc. All rights reserved.
URI
https://scholarworks.unist.ac.kr/handle/201301/32188
URL
https://www.sciencedirect.com/science/article/pii/S002203962030022X?via%3Dihub
DOI
10.1016/j.jde.2020.01.016
ISSN
0022-0396
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PHY_Journal Papers
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