Article
Mechanics
Chuong V. Tran, Xinwei Yu, David G. Dritschel
Summary: Incompressible fluid flows are characterized by high correlations between velocity and pressure, as well as between vorticity and pressure. This correlation plays a significant role in maintaining regularity in Navier-Stokes flows. The study suggests that as long as global pressure minimum (or minima) and velocity maximum (or maxima) are mutually exclusive, regularity is likely to persist.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics, Applied
Yanqing Wang, Yulin Ye
Summary: In this paper, an energy conservation criterion is derived for weak solutions of both the incompressible and compressible Navier-Stokes equations. The criterion is based on a combination of velocity and its gradient. For the incompressible case, it extends known results on periodic domain, including the famous Lions' energy conservation criterion. For the compressible case, it improves recent results and extends criteria for energy conservation from incompressible to compressible flow.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Juan Vicente Gutierrez-Santacreu, Marko Antonio Rojas-Medar
Summary: The Navier-Stokes-alpha equations are a type of LES models that aim to capture the influence of small scales on large ones without calculating the entire flow range. The parameter α represents the smallest resolvable scale by the model. When α=0, the classical Navier-Stokes equations for viscous, incompressible, Newtonian fluids are recovered. These equations can also be seen as a regularization of the Navier-Stokes equations, where α stands for the regularization parameter.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mechanics
Yuri V. Lvov, Victor S. L'vov
Summary: The researchers used the Dyson-Wyld diagrammatic technique to analyze the infinite series for the correlation functions of velocity in hydrodynamic turbulence. They found that the triple correlator of velocity plays a fundamental role in determining the statistical characteristics of the turbulence. All higher-order correlation functions can be expressed through the triple correlator. The study also showed that the suggested triangular re-summation of the infinite diagrammatic series can explain why the inverse cascade of two-dimensional hydrodynamic turbulence is close to Gaussian, supporting the idea that the flux of energy is one of the main characteristics of hydrodynamic turbulence, as proposed by Kolmogorov in 1941.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
Mengze Wang, Gregory L. Eyink, Tamer A. Zaki
Summary: Boundary-layer transition is rigorously explained using the stochastic Lagrangian formulation of the Navier-Stokes equations, and the increase in skin friction is analyzed. It is found that the stretching of near-wall spanwise vorticity is the dominant source of increased skin friction during laminar-to-turbulent transition.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Warren R. Smith, Qianxi Wang
Summary: Small viscous effects in high-Reynolds-number rotational flows accumulate over time to have a leading-order effect, making the high-Reynolds-number limit for the Navier-Stokes equations singular. Investigating whether a solution of the Euler equations can approximate a real flow at large Reynolds number is crucial. The neglect of these facts leads to the use of Euler equations to simulate laminar rotational flows at large Reynolds number.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Milad Azari, Arman Sadeghi
Summary: The paper theoretically studies the unsteady dispersion of a solute band in a semicircular microchannel under a steady pressure-driven flow. Analytical solutions are obtained for the exchange, convection, and dispersion coefficients as well as the solute concentration and mean solute concentration. The study investigates the influences of the initial concentration distribution and the reaction rate on the transport coefficients.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mathematics, Applied
Minghao Li, Liuchao Xiao, Zhenzhen Li
Summary: In this paper, the supercloseness properties and global superconvergence results for the implicit Euler scheme of the transient Navier-Stokes equations are derived. The supercloseness properties of the Stokes projection for velocity and pressure are deduced based on a prior estimate of finite element solutions, properties of the Stokes projection and operator, derivative transforming skill, and H-1-norm estimate. The supercloseness properties of the interpolation operators for two pairs of rectangular elements are obtained, and global superconvergence results are achieved through interpolation postprocessing technique.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics, Applied
Thomas Eiter, Giovanni P. Galdi
Summary: The study focuses on the asymptotic spatial behavior of the vorticity field associated with a time-periodic Navier-Stokes flow past a body, showing exponential decay outside the wake region and faster decay inside it. This implies that the vorticity field behaves like that of the corresponding steady-state problem sufficiently far from the body.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Physics, Mathematical
Xiangming Zhu, Chengkui Zhong
Summary: The existence and structure of L-p uniform attractors for reaction-diffusion equations with a larger class of external forces are considered. A new class of external forces g, larger than the class of normal functions, is introduced. The existence and structure of the uniform (L-2-L-p) attractors are obtained by investigating the property of the hull H(g) and using prior estimates.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Mathematical
Helin Guo, Lingling Zhao
Summary: In this paper, the regularity criteria for three-dimensional nematic liquid crystal flows are shown. It is proved that the strong solution can be extended under certain conditions. This result is of great significance for the study of liquid crystal dynamics.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Mathematical
Dongho Chae
Summary: In this paper, we study the Liouville type problem for stationary magnetohydrodynamic equations in R-n. We prove that the solution is trivial under certain anisotropic integrability conditions on the components of the velocity and the magnetic field.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Physics, Mathematical
Xinghong Pan
Summary: This paper studies Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab and proves the trivialness of the velocity and the magnetic field under various boundary conditions. Five types of boundary conditions are considered, and one innovation is the absence of a finite Dirichlet integral assumption on the magnetic field compared with previous works.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mechanics
Shisheng Wang
Summary: Through studying, it is found that both the mass conservation and Navier-Stokes equations are Galilean invariant in any arbitrary inertial reference frame, and the speed of pressure wave depends on the thermodynamic equation of state of the fluid, regardless of the fluid element velocity. When the local Mach number is one, the extended Navier-Stokes equations will exhibit an intrinsic singularity, indicating the transition from subsonic flow to supersonic flow.
Article
Mathematics
Dallas Albritton, Tobias Barker, Christophe Prange
Summary: This article establishes a local-in-space short-time smoothing effect for the Navier-Stokes equations in the half space, overcoming the challenge of stronger non-local pressure effects. The application demonstrates that the critical L3x norm must concentrate at scales similar to root T* - t in the presence of a Type I blow-up.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Marcone C. Pereira, Ricardo P. Silva
QUARTERLY OF APPLIED MATHEMATICS
(2015)
Article
Mathematics
Ricardo P. Silva
MONATSHEFTE FUR MATHEMATIK
(2016)
Article
Mathematics, Applied
E. M. Bonotto, J. G. Mesquita, R. P. Silva
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2018)
Article
Mathematics
Ricardo P. Silva
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
(2014)
Article
Mathematics, Applied
Marcone C. Pereira, Ricardo P. Silva
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2013)
Article
Mathematics, Applied
E. Capelato, K. Schiabel-Silva, R. P. Silva
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2013)
Article
Mathematics, Applied
Jose M. Arrieta, Alexandre N. Carvalho, Marcone C. Pereira, Ricardo P. Silva
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2011)
Article
Mathematics, Applied
Jamil V. Pereira, Ricardo P. Silva
BOUNDARY VALUE PROBLEMS
(2013)
Article
Mathematics
Ricardo Parreira da Silva
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
(2020)
Proceedings Paper
Mathematics, Applied
Marcone C. Pereira, Ricardo P. Silva
CONTRIBUTIONS TO NONLINEAR ELLIPTIC EQUATIONS AND SYSTEMS
(2015)
Article
Mathematics
Ricardo P. Silva
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
(2015)
Article
Mathematics, Applied
Ricardo Parreira da Silva
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2012)
Article
Mathematics, Applied
Vera Lucia Carbone, Marcelo Jose Dias Nascimento, Karina Schiabel-Silva, Ricardo Parreira da Silva
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2011)
Article
Mathematics, Applied
Ricardo P. Silva
INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS
(2013)