Mongi Blel, Jamel Benameur
In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $α|u|^{β-1}u(α>0,\;β\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the continuity in $L^2$ for $β>3$, also the large time decay is proved for $β\geq\frac{10}3$. Fourier analysis and standard techniques are used.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).
We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with the nonlinear exponential damping term $a (e^{b |u|^{\bf 2}}-1)u$, ($a,b>0$) studied by the second author in \cite{J1}.
In this paper we prove the existence and uniqueness of strong solution of the incompressible Navier-Stokes equations with damping $α(e^{β|u|^2}-1)u$.
Generalization of 3D-NSE Global Weak Solution with damping
本文推广了带阻尼项的3D不可压缩Navier-Stokes方程，证明了其全局弱解的存在性、唯一性及在L^2中的连续性，其中阻尼函数为递增凸可微且零点为零。
In this paper we prove the global existence of incompressible Navier-Stokes equations with damping $α(e^{β|u|^2}-1)u$, where we use Friedrich method and some new tools. The delicate problem in the construction of a global solution, is the passage to the limit in exponential nonlinear term. To solve this problem, we use a polynomial approximation of the damping part and a new type of interpolation between $L^\infty(\mathbb{R}^+,L^2(\mathbb{R}^3))$ and the space of functions $f$ such that $(e^{β|f|^2}-1)|f|^2\in L^1(\mathbb{R}^3)$. Fourier analysis and standard techniques are used.
When a Leray--Hopf weak solution to the NSE has a singularity set $S$ of dimension $d$ less than $3$---for example, a suitable weak solution---we find a family of new $L^q L^p$ conditions that guarantee validity of the energy equality. Our conditions surpass the classical Lions--Ladyženskaja $L^4 L^4$ result in the case $d<1$. Additionally, we establish energy equality in certain cases of Type-I blowup. The results are also extended to the NSE with fractional power of the Laplacian below $1$.
Non-Leray-Hopf solutions to 3D stochastic hyper-viscous Navier-stokes equations: beyond the Lions exponents
研究三维随机超粘性Navier-Stokes方程，证明在超越Lions指数的高粘性区域，尽管Leray-Hopf类中解唯一，但在混合Lebesgue空间中存在无穷多个非Leray-Hopf解，并建立了噪声消失极限结果。
In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in {\textit{all Gevrey classes}}. This strengthens the previous result obtained in Sobolev spaces by Foias-Saut. By using the Gevrey-norm technique of Foias-Temam, the proof of our improved result simplifies the original argument of Foias-Saut, thereby, increasing its adaptability to other d…
In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution ${\mathbf u}$ of 3D-NSE and each $(s,x)\in\mathbb{R}_+\times\mathbb{R}^3$, we show the existence of weak solutions to the following SDE, which has a density $ρ_{s,x}(t,y)$ belonging to $\mathbb{H}^{1,p}_q$ provided $p,q\in[1,2)$ with $\frac{3}{p}+\frac{2}{q}>4$: $$ \mathrm{d} X_{s,t}={\mathbf u} (s,X_{s,t})\mathrm{d} t+\sqrt{2ν}\mathrm{d} W_t,\ \ X_{s,s}=x,\ \ t\geq s, $$ where $W$ is a three dimensional standard Brownian …
In the classic work of Beale-Kato-Majda ({[}2{]}) for the Euler equations in $\mathbb{R^{\mathrm{3}}}$, regularity of a solution throughout a given interval $[0,T_{*}]$ is obtained provided that the curl $ω$ satisfies $ω\in L^{1}((0,T);L^{\infty}(\mathbb{R^{\textrm{\ensuremath{3}}}})$ for all $T<T_{*}$, and the arguments apply equally well to the Navier-Stokes equations (NSE) in $\mathbb{R^{\mathrm{3}}}$. The spatial $L^{\infty}$-criterion imposed on the curl was generalized to other function spaces by various authors ({[}9{]}, {[}10{]}, {[}11{]}). In {[}8{]} regularity results of this type ar…
In this paper, we provide conditions, \emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf weak solutions of the three dimensional Navier-Stokes equations (3D NSE). The aforementioned conditions on the observations, which in this case comprise either of \emph{modal} or \emph{volume element observations}, are automatically satisfied for solutions that are globally regular and are uniformly bounded in the $H^1$-norm. However, neither regularity nor uniqueness is ne…
The long time behavior of Wong-Zakai approximations of 2D as well as 3D non-autonomous stochastic convective Brinkman-Forchheimer (CBF) equations with non-linear diffusion terms on bounded and unbounded ($\mathbb{R}^d$ for $d=2,3$) domains is discussed in this work. To establish the existence of random pullback attractors, the concept of asymptotic compactness (AC) is used. In bounded domains, AC is proved via compact Sobolev embeddings. In unbounded domains, due to the lack of compact embeddings, the ideas of energy equations and uniform tail estimates are exploited to prove AC. In the litera…
Uniform global attractors for the nonautonomous 3D Navier-Stokes equations
该研究针对含平移有界外力的非自治三维Navier-Stokes方程，通过构造无唯一性自治演化系统闭包的方法，得到弱一致全局吸引子的存在性与结构，建立了可推广至其他非自治耗散偏微分方程的通用框架。
The incompressible Toner-Tu (ITT) partial differential equations (PDEs) are an important example of a set of active-fluid PDEs. While they share certain properties with the Navier-Stokes equations (NSEs), such as the same scaling invariance, there are also important differences. The NSEs are usually considered in either the decaying or the additively forced cases, whereas the ITT equations have no additive forcing. Instead, they include a linear, activity term $α\bu$ ($\bu$ is the velocity field) which pumps energy into the system, but also a negative $\bu|\bu|^{2}$-term which provides a platf…
Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic Multi-Compartment Head Model
本文提出基于 Navier-Stokes 方程和 Carreau-Yasuda 模型的非牛顿脑血流动态建模方法，结合 Fick 定律与 Archie 定律，在真实多隔室头部模型中近似血流及电导率分布，适用于先验信息有限的任意可区分动脉的头部模型。
Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations
该研究针对三维不可压缩纳维-斯托克斯方程，引入局域 coercivity 性质，在非自治框架下建立指数能量衰减，并提出有限维谱量作为 coercivity 的可计算代理，为降阶模型给出显式衰减估计。
Mathematical study of a new Navier-Stokes-alpha model with nonlinear filter equation -- Part I
本文首次理论分析带非线性滤波方程的新型 Navier-Stokes-alpha 耦合系统，证明弱解存在唯一性、向经典解收敛及全局吸引子分形维数界。
Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
本文通过理论、数值和机器学习方法研究偏微分方程中的奇点形成问题，提出新的分析框架和数值方法，提升对复杂方程中奇点形成机制的理解与预测能力。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。