Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces

Autor: Alexey Cheskidov, Xiaoyutao Luo

Publikováno v: Nonlinearity. 33:1388-1403

Onsager's conjecture for the 3D Navier–Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note, we establish the energy equality for weak solutions in a large class of function spac

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::38c711d8a37c15050a460eae4770e38d
https://doi.org/10.1088/1361-6544/ab60d3

Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier–Stokes equations

Autor: Mimi Dai, Alexey Cheskidov

Publikováno v: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 149:429-446

Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional fluid flow. A determining wavenumber, first introduced

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19769e573f6e4aae438f4cc0cc298205
https://doi.org/10.1017/prm.2018.33

The Existence of a Global Attractor for the Forced Critical Surface Quasi-Geostrophic Equation in $$L^2$$ L 2

Autor: Alexey Cheskidov, Mimi Dai

Publikováno v: Journal of Mathematical Fluid Mechanics. 20:213-225

We prove that the critical surface quasi-geostrophic equation driven by a force f possesses a compact global attractor in $$L^2(\mathbb T^2)$$ provided $$f\in L^p(\mathbb T^2)$$ for some $$p>2$$ . First, the De Giorgi method is used to obtain uniform

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::28bdff019a39a591f6ebccf8232300fe
https://doi.org/10.1007/s00021-017-0324-7

Local estimates of Hölder exponents in turbulent vector fields

Autor: Alexey Cheskidov, Pierre Kestener, Bérengère Dubrulle, Florian Nguyen, Jean-Philippe Laval, Roman Shvydkoy

Publikováno v: Physical Review E
Physical Review E, American Physical Society (APS), 2019, 99 (5), ⟨10.1103/PhysRevE.99.053114⟩
Physical Review E, 2019, 99 (5), ⟨10.1103/PhysRevE.99.053114⟩

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some expon

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9adb7500b0daad1d0e4fe895a4d28b27
https://pubmed.ncbi.nlm.nih.gov/31212522

Energy Conservation in Two-dimensional Incompressible Ideal Fluids

Autor: M. C. Lopes Filho, Alexey Cheskidov, H. J. Nussenzveig Lopes, Roman Shvydkoy

Publikováno v: Communications in Mathematical Physics. 348:129-143

This note addresses the issue of energy conservation for the 2D Euler system with an L p -control on vorticity. We provide a direct argument, based on a mollification in physical space, to show that the energy of a weak solution is conserved if $${\o

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https://doi.org/10.1007/s00220-016-2730-8