arXiv subjects

Pedro Gabriel Fernández Dalgo

Publications and source records attributed to Pedro Gabriel Fernández Dalgo.

4 recordsLinked to original sources

arXiv2026

Global Yudovich-type solutions to a reduced model for micropolar fluids with zero viscosity

In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation for the two-dimensional velocity field of the fluid and an advection-diffusion equation for the scalar microrotation field. For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded and of finite energy. To the best of our knowledge, this is the first result which extends the genuine Yudovich framework to a system obtained by perturbing the incompressible Euler equations with some sort of heterogeneity.

math.AP↗

arXiv2025

Dynamic Refinement of Pressure Decomposition in Navier-Stokes Equations

In this work, the local decomposition of pressure in the Navier-Stokes equations is dynamically refined to prove that a relevant critical energy of a suitable Leray-type solution inside a backward paraboloid -- regardless of its aperture -- is controlled near the vertex by a critical behavior confined to a neighborhood of the paraboloid's boundary. This neighborhood excludes the interior near the vertex and remains separated from the temporal profile of the vertex, except at the vertex itself. Then, we present a refined scaling invariant regularity result.

math.AP↗

arXiv2025

Micropolar fluids with initial angular velocities in non-homogeneous Sobolev spaces of order $-1/2$

In this paper, we investigate fractional energy methods for Micropolar fluids, starting with an initial angular velocity of negative Sobolev regularity. For the initial angular velocity assumption, we consider a non-homogeneous Sobolev norm of negative order. The regularity -1/2 studied here corresponds to the critical scaling of a simplified associated system, and the general framework can also be applied to the Boussinesq system with viscosity. Since our approach differs from those based on mild solutions and does not rely on a projected system, this work provides new tools for studying the Caffarelli-Kohn-Nirenberg theory of singularities in coupled variables within the Navier-Stokes equations.

math.AP↗

arXiv2024

Mild solutions to the 3D-Boussinesq system with weakened initial temperature

In this research, the Cauchy problem of the 3D viscous Boussinesq system is studied considering an initial temperature with negative Sobolev regularity. Precisely, we construct local in time mild solutions to this system where the temperature term belongs to Sobolev spaces of negative order. Our main contribution is to show how the coupled structure of the Boussinesq system allows us to considerably weaken the regularity in the temperature term.

math.AP↗