Zobrazeno 1 - 10
of 129
pro vyhledávání: '"Cheskidov, Alexey"'
The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data there exist infinitely many global in time weak solutions with smooth ener
Externí odkaz:
http://arxiv.org/abs/2407.17463
Autor:
Cheskidov, Alexey, Peng, Qirui
We introduce a determining wavenumber for weak solutions of 3D Navier-Stokes equations whose time average is bounded by Kolmogorov dissipation wavenumber over the whole range of intermittency dimensions. This improves previous works by Cheskidov, Dai
Externí odkaz:
http://arxiv.org/abs/2407.06474
Autor:
Cheskidov, Alexey
Dissipation anomaly, a phenomenon predicted by Kolmogorov's theory of turbulence, is the persistence of a non-vanishing energy dissipation for solutions of the Navier-Stokes equations as the viscosity goes to zero. Anomalous dissipation, predicted by
Externí odkaz:
http://arxiv.org/abs/2311.04182
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were obtained in the past one hundred years, including t
Externí odkaz:
http://arxiv.org/abs/2209.10203
Autor:
Cheskidov, Alexey, Luo, Xiaoyutao
In this paper, we revisit the notion of temporal intermittency to obtain sharp nonuniqueness results for linear transport equations. We construct divergence-free vector fields with sharp Sobolev regularity $L^1_t W^{1,p}$ for all $p<\infty$ in space
Externí odkaz:
http://arxiv.org/abs/2204.08950
Autor:
Cheskidov, Alexey, Shvydkoy, Roman
This study introduces a new family of volumetric flatness factors which give a rigorous parametric description of the phenomenon of intermittency in fully developed turbulent flows. These quantities gather information about the most "active" part of
Externí odkaz:
http://arxiv.org/abs/2203.11060
Autor:
Cheskidov, Alexey, Dai, Mimi
We estimate the number of degrees of freedom of solutions of the 2D Navier-Stokes equation, proving that its mathematical analog, the number of determining modes, is bounded by the Kraichnan number squared. In particular, this provides new bounds on
Externí odkaz:
http://arxiv.org/abs/2112.11606
Autor:
Cheskidov, Alexey, Luo, Xiaoyutao
In this paper, we consider the 2D incompressible Navier-Stokes equations on the torus. It is well known that for any $L^2$ divergence-free initial data, there exists a global smooth solution that is unique in the class of $C_t L^2$ weak solutions. We
Externí odkaz:
http://arxiv.org/abs/2105.12117
Autor:
Cheskidov, Alexey, Luo, Xiaoyutao
In this paper, we prove a sharp nonuniqueness result for the incompressible Navier-Stokes equations in the periodic setting. In any dimension $d \geq 2$ and given any $ p<2$, we show the nonuniqueness of weak solutions in the class $L^{p}_t L^\infty$
Externí odkaz:
http://arxiv.org/abs/2009.06596
Autor:
Cheskidov, Alexey, Luo, Xiaoyutao
We consider the linear transport equations driven by an incompressible flow in dimensions $d\geq 3$. For divergence-free vector fields $u \in L^1_t W^{1,q}$, the celebrated DiPerna-Lions theory of the renormalized solutions established the uniqueness
Externí odkaz:
http://arxiv.org/abs/2004.09538