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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,109 - 1,127 (19page)
- DOI
- 10.4134/BKMS.b200470
이용수
초록· 키워드
오류제보하기
We study the long-term dynamics for a family of incompressible three-dimensional Leray-$\alpha$-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-$\alpha$ model when varying two nonnegative parameters $\theta_1$ and $\theta_2$. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-$\alpha$-like models into a finite-dimensional space is determining if it annihilates the difference of two ``nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.
목차
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참고문헌 (24)
참고문헌 신청
Hani Ali / 2013 / On a critical Leray- model of turbulence / Nonlinear Analysis: Real World Applications 14(3):1563~1584
Hani Ali / 2013 / Mathematical Results for Some α Models of Turbulence with Critical and Subcritical Regularizations / Journal of Mathematical Fluid Mechanics 15(2):303~316
David Barbato / 2014 / Global regularity for a slightly supercritical hyperdissipative Navier–Stokes system / Analysis & PDE 7(8):2009~2027
Alexey Cheskidov / 2005 / On a Leray–α model of turbulence / Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461(2055):629~649
Bernardo Cockburn / 1997 / Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems / Mathematics of Computation 66(219):1073~1087
Hani Ali / 2013 / Mathematical Results for Some α Models of Turbulence with Critical and Subcritical Regularizations / Journal of Mathematical Fluid Mechanics 15(2):303~316
David Barbato / 2014 / Global regularity for a slightly supercritical hyperdissipative Navier–Stokes system / Analysis & PDE 7(8):2009~2027
Alexey Cheskidov / 2005 / On a Leray–α model of turbulence / Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461(2055):629~649
Bernardo Cockburn / 1997 / Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems / Mathematics of Computation 66(219):1073~1087
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