The large-scale structure of many turbulent flows encountered in practical situations such as
aeronautics, industry, meteorology is nowadays successfully computed using the …

With the rapid development of generative artificial intelligence, particularly large language
models, a number of sub-fields of deep learning have made significant progress and are …

In this paper we exclude the scenario of rotated discretely self-similar singularities of the 3D
incompressible Euler equations in the case when the singularity point is isolated and the …

We study the backward discretely self-similar solutions to the generalized Euler equations,
where usual Biot-Savart kernel representing the velocity in terms of the vorticity is replaced …

We establish existence of solutions in a scale of classes weaker than the finite energy Leray
class and stronger than the infinite energy Lemarié-Rieusset class. The new classes are …

First, we discuss the non-Gaussian type of self-similar solutions to the Navier–Stokes
equations. We revisit a class of self-similar solutions which was studied in Canonne et …

For the incompressible Navier-Stokes system, when initial data are uniformly locally square
integral, the local existence of solutions has been obtained. In this paper, we consider …

The question of whether the hyper-dissipative (HD) Navier-Stokes (NS) system can exhibit
spontaneous formation of singularities in the super-critical regime--the hyper-dissipation …

This article examines the Bouton–Lie group invariants of the Navier–Stokes equation (NSE)
for incompressible fluids. The theory is applied to the general scaling transformation …

In this article, we consider the existence of discretely self-similar solutions and self-similar
solutions to the 3D generalized magnetohydrodynamics (MHD) system with fractional …