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Pedro Gabriel Fernández-Dalgo

Publications and source records attributed to Pedro Gabriel Fernández-Dalgo.

6 recordsLinked to original sources
arXiv2023

Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity

In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the critical Lebesgue norm in general or the critical weak Lebesgue norm in the axisymmetric case. This type of results is inspired in particular by a work of Neustupa (2014), which handles certain non endpoint critical norms. Our work enables to have a better understanding of the nonlocal effect of the pressure on the regularity of the solutions.

math.AP↗
arXiv2021

Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl

We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) -- $γ$ 2 dx), with r = x 2 1 + x 2 2 and $γ$ $\in$ (0, 2).

math.AP↗
arXiv2020

Weak-strong uniqueness in weighted $L^2$ spaces and weak suitable solutions in local Morrey spaces for the MHD equations

We consider here the magneto-hydrodynamics (MHD) equations on the whole space. For the 3D case, in the setting of the weighted $L^2$ spaces we obtain a weak-strong uniqueness criterion provided that the velocity field and the magnetic field belong to a fairly general multipliers space. On the other hand, we study the local and global existence of weak suitable solutions for intermittent initial data, which is characterized through a local Morrey space. This large initial data space was also exhibit in a contemporary work [4] in the context of 3D Navier-Stokes equations. Finally, we make a discussion on the local and global existence problem in the 2D case.

math.AP↗
arXiv2019

Existence of infinite-energy and discretely self-similar global weak solutions for 3D MHD equations

This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces $L^2_{w_γ}$, with $w_γ(x)=(1+| x|)^{-γ}$ and $0 \leq γ\leq 2$. Moreover, we prove the existence of discretely self-similar solutions for 3D MHD equations for discretely self-similar initial data which are locally square integrable. Our methods are inspired of a recent work of P. Fernández-Dalgo and P.G. Lemarié-Riseusset for the 3D Navier-Stokes equations.

math.AP↗
arXiv2019

Weak solutions for Navier--Stokes equations with initial data in weighted $L^2$ spaces

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 w$γ$ , where w $γ$ (x) = (1 + |x|) --$γ$ and 0 < $γ$ $\le$ 2, using new energy controls. As application we give a new proof of the existence of global weak discretely self-similar solutions of the 3D Navier-Stokes equations for discretely self-similar initial velocities which are locally square inte-grable.

math.AP↗