[کتاب][B] The Navier-Stokes problem in the 21st century

PG Lemarié-Rieusset - 2018‏ - taylorfrancis.com
Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

[کتاب][B] Fourier analysis and nonlinear partial differential equations

H Bahouri - 2011‏ - Springer
Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

[کتاب][B] Navier-Stokes equations and turbulence

C Foias, O Manley, R Rosa, R Temam - 2001‏ - books.google.com
This book aims to bridge the gap between practising mathematicians and the practitioners of
turbulence theory. It presents the mathematical theory of turbulence to engineers and …

Remark on the rate of decay of higher order derivatives for solutions to the Navier–Stokes equations in Rn

M Oliver, ES Titi - Journal of Functional Analysis, 2000‏ - Elsevier
We present a new derivation of upper bounds for the decay of higher order derivatives of
solutions to the unforced Navier–Stokes equations in R n. The method, based on so-called …

Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology

VR Martinez, Z Wang, K Zhao - Indiana University Mathematics Journal, 2018‏ - JSTOR
In this paper, we study the qualitative behavior of the Cauchy problem of a hyperbolic model
\left{p_t-∇⋅\left(pq\right)\,=\,Δp,\,x∈\CalR^d,t>0,\hfillq_t-∇\left(ε|q|^2+p\right)\,=\,εΔq,\hfill\cr …

Analyticity and decay estimates of the Navier–Stokes equations in critical Besov spaces

H Bae, A Biswas, E Tadmor - Archive for Rational Mechanics and Analysis, 2012‏ - Springer
In this paper, we establish analyticity of the Navier–Stokes equations with small data in
critical Besov spaces ̇ B^ 3 p-1 _ p, q. The main method is Gevrey estimates, the choice of …

Skin friction and pressure: the “footprints” of turbulence

TR Bewley, B Protas - Physica D: Nonlinear Phenomena, 2004‏ - Elsevier
The problems of exact state reconstruction and approximate state estimation based on wall
information in a wall-bounded incompressible unsteady flow are addressed. It is shown that …

Higher-order synchronization for a data assimilation algorithm for the 2D Navier–Stokes equations

A Biswas, VR Martinez - Nonlinear Analysis: Real World Applications, 2017‏ - Elsevier
We consider the two-dimensional (2D) Navier–Stokes equations (NSE) with space periodic
boundary conditions and an algorithm for continuous data assimilation developed by …

On the radius of analyticity of solutions to the three-dimensional Euler equations

I Kukavica, V Vicol - Proceedings of the American Mathematical Society, 2009‏ - ams.org
We address the problem of analyticity of smooth solutions $ u $ of the incompressible Euler
equations. If the initial datum is real–analytic, the solution remains real–analytic as long as …

Singularities of Euler flow? Not out of the blue!

U Frisch, T Matsumoto, J Bec - Journal of statistical physics, 2003‏ - Springer
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a
singularity with infinite vorticity after a finite time? This blowup problem is still open. After …