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math.AP2022
Renormalization and existence of the finite-time blow up solutions for a one-dimensional analogue of the Navier-Stokes equations
Denis Gaidashev, Alejandro Luque
The one-dimensional quasi-geostrophic equation is the one-dimensional Fourier-space analogue of the famous Navier-Stokes equations. In their work Li and Sinai have proposed a renor…
math.DS2022
Universality but no rigidity for two-dimensional perturbations of almost commuting pairs
D. Gaidashev, D. Lilja
In this paper we consider two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. It has been shown earlier that such…
math.AP2022
Renormalization and a-priori bounds for Leray self-similar solutions to the generalized mild Navier-Stokes equations
Denis Gaidashev
We demonstrate that the problem of existence of Leray self-similar blow up solutions in a generalized mild Navier-Stokes system with the fractional Laplacian can be st…