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 作者：Ciprian Foias , Michael S. Jolly , Dan Lithio ... 来源：[J].Journal of Nonlinear Science(IF 1.566), 2017, Vol.27 (5), pp.1513-1529 摘要：The evolution of a determining form for the 2D Navier–Stokes equations (NSE) which is an ODE on a space of trajectories is completely described. It is proved that at every stage of its evolution, the solution is a convex combination of the initial trajectory and a chosen, fi...
 作者：Cheng Yu 来源：[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2017, Vol.225 (3), pp.1073-1087 摘要：In this paper, we prove the energy conservation for the weak solutions of the compressible Navier–Stokes equations for any time t > 0, under certain conditions. The results hold for the renormalized solutions of the equations with constant viscosities, as well as the weak so...
 作者：Dongho Chae , Jörg Wolf 来源：[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2017, Vol.225 (1), pp.549-572 摘要：We prove Liouville type theorems for the self-similar solutions to the Navier–Stokes equations. One of our results generalizes the previous ones by Nečas–Ru̇žička–Šverák and Tsai. Using a Liouville type theorem, we also remove a scenario of asymptotically self-sim...
 作者：Igor Kukavica , Walter Rusin , Mohammed Ziane 来源：[J].Journal of Nonlinear Science(IF 1.566), 2017, Vol.27 (6), pp.1725-1742 摘要：We establish a sufficient regularity condition for local solutions of the Navier–Stokes equations. For a suitable weak solution ( u , p ) on a domain D we prove that if $$\partial _3 u$$ belongs to the space $$L_t^{s_0}L_x^{r_0}(D)$$ where $$2/s_0 + 3/r_0 \le 2$$ and \(9/4 \l...
 作者：Animikh Biswas , Ciprian Foias , Basil Nicolaenko 来源：[J].Physica D: Nonlinear Phenomena(IF 1.669), 2018, Vol.376-377, pp.5-14 摘要：Abstract(#br)Gevrey class technique is a widely used tool for studying higher regularity properties of solutions to dissipative equations. Maximal radius in a Gevrey class determines a small length scale associated to the decay of the Fourier power spectrum and turbulence. In ...
 作者：Yong Lu , Sebastian Schwarzacher 来源：[J].Journal of Differential Equations(IF 1.48), 2018, Vol.265 (4), pp.1371-1406 摘要：Abstract(#br)We consider the homogenization problem of the compressible Navier–Stokes equations in a bounded three dimensional domain perforated with very tiny holes. As the number of holes increases to infinity, we show that, if the size of the holes is small enough, the ho...
 作者：Bo-Qing Dong , Yan Jia 来源：[J].Nonlinear Analysis: Real World Applications(IF 2.201), 2016, Vol.30, pp.41-58 摘要：Abstract(#br)This paper is devoted to the investigation of stability behaviors of Leray weak solutions to the three-dimensional Navier–Stokes equations. For a Leray weak solution of the Navier–Stokes equations in a critical Besov space, it is shown that the Leray weak solut...
 作者：Ruili Wen , Shugen Chai 来源：[J].Applied Mathematics Letters(IF 1.501), 2020, Vol.101 摘要：Abstract(#br)This paper studies the decay and the asymptotic behavior of solutions to the 3D incompressible Navier–Stokes equations with nonlinear damping α | u | β − 1 u ( α > 0 , β > 1 ) . We will prove the L 2 decay of weak solutions for β > 1 with any α > 0 . Mo...
 作者：Chenyin Qian 来源：[J].Nonlinear Analysis: Real World Applications(IF 2.201), 2020, Vol.54 摘要：Abstract(#br)The anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient ( ∂ i u j , 1 ≤ i , j ≤ 3 ) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of...
 作者：Myong-Hwan Ri 来源：[J].Nonlinear Analysis(IF 1.64), 2020, Vol.190 摘要：Abstract(#br)In this paper, we prove that a Leray–Hopf weak solution u to 3D Navier–Stokes equations is regular if L ∞ ( 0 , T ; B ̇ ∞ , ∞ − 1 ) -norm of a suitable low frequency part of u is bounded by a scaling invariant constant depending on the kin...