Navier-Stokes Equations with Potentials by Adriana-Ioana Lefter

“…We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. …”
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On Unique Continuation for Navier-Stokes Equations by Zhiwen Duan, Shuxia Han, Peipei Sun

“…We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. …”
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On the Navier-Stokes equations with temperature-dependent transport coefficients by Eduard Feireisl, Josef Málek

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A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces by Xiang'ou Zhu

“…We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to 𝐿2/(2−𝑟)̇𝐻((0,𝑇);ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3))), where ̇𝐻ℳ(𝑟(ℝ3̇𝐻)→−𝑟(ℝ3)) is the multipliers between Sobolev spaces whose definition is given later for 0<𝑟<1, then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular.…”
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Analytical Solution to 1D Compressible Navier-Stokes Equations by Changsheng Dou, Zishu Zhao

“…There exist complex behavior of the solution to the 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x,t∈0,+∞×R+, that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.…”
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Asymptotic Behavior of the Solutions of the Generalized Globally Modified Navier–Stokes Equations by Yonghong Duan, Xiaojuan Chai

“…The paper is concerned with the existence and the asymptotic behavior of solutions to a class of generalized Navier–Stokes equations, which generalises the so-called globally modified Navier–Stokes equations. …”
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The New Semianalytical Technique for the Solution of Fractional-Order Navier-Stokes Equation by Nehad Ali Shah, Mounirah Areshi, Jae Dong Chung, Kamsing Nonlaopon

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Wave turbulence: a solvable problem applied to the Navier–Stokes equations by Galtier, Sébastien

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A Semianalytical Approach to the Solution of Time-Fractional Navier-Stokes Equation by Zeeshan Ali, Shayan Naseri Nia, Faranak Rabiei, Kamal Shah, Ming Kwang Tan

“…In this manuscript, a semianalytical solution of the time-fractional Navier-Stokes equation under Caputo fractional derivatives using Optimal Homotopy Asymptotic Method (OHAM) is proposed. …”
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An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form by Jia Liu

“…We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. …”
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Stabilized Multiscale Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations by Tong Zhang, Shunwei Xu, Jien Deng

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Global Existence of the Cylindrically Symmetric Strong Solution to Compressible Navier-Stokes Equations by Jian Liu, Ruxu Lian

“…This paper is concerned with the initial boundary value problem for the three-dimensional Navier-Stokes equations with density-dependent viscosity. …”
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Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise by Xiaoyao Jia, Xiaoquan Ding

“…In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. …”
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A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space by Xunwu Yin

“…This paper is concerned with the regularity of Leray weak solutions to the 3D Navier-Stokes equations in Lorentz space. It is proved that the weak solution is regular if the horizontal velocity denoted by ũ=(u1,u2,0) satisfies ũ(x,t)∈Lq(0,T;Lp,∞(R3))  for  2/q + 3/p=1,  3<p<∞. …”
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Maximum Norm Estimates of the Solution of the Navier-Stokes Equations in the Halfspace with Bounded Initial Data by Santosh Pathak

“…In this paper, I consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝ+n for n≥3 with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. …”
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Computer Simulation of Water Flow Animation Based on Two-Dimensional Navier-Stokes Equations by Rushi Cao, Ruyun Cao

“…Based on the two-dimensional Navier-Stokes equations, a mathematical model is established to solve the boundary conditions required by the physical flow field of water. …”
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Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations by Junbai Ren

“…This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1. …”
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Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping by Xin-Guang Yang, Jun-Tao Li

“…Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.…”
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Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition by Hicham Mahdioui, Sultana Ben Aadi, Khalid Akhlil

“…In this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. …”
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The Double-Logarithmic Regularity Criterion of Pressure for the 3D Navier–Stokes Equations in the Besov Space by Min Liu, Juan Song, Tian-Li Li

“…Our main result is the double-logarithmic regularity criterion of pressure for the 3D Navier–Stokes equations in the Besov space. ∫0TπB˙∞,∞−3/qp/e+lne+πB˙∞,∞−3/qlne+lne+πB˙∞,∞−3/qdt<∞, 2/q+3/q=2,3≤q≤∞. …”
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