Luis Mart'inez-Zoroa

activity

20212026

most citedNon Existence and Strong Ill-Posedness in

H^{2}

for the Stable IPM Equation

1 citations · 3 across the 15 of their papers we have counts for

collaborators

16 papers

math.AP2026

Non Existence of the Stable 2D Boussinesq Equations in $H^{2}$ via Density-Vorticity Feedback

Roberta Bianchini, Luis Martínez-Zoroa

We establish instantaneous $H^{2}$ norm explosion for the two-dimensional Boussinesq equations around the linearly stable background profile $- x_{2}$ . While previous ill-posedness resu…

math.AP2026

Blow-up at finite time for the generalized SQG equations in the Sobolev well-posedness regime

Diego Córdoba, Óscar Domínguez, José Lucas-Manchón +1

We prove finite-time singularity formation for the forced generalized surface quasi-geostrophic equation in the singular velocity regime $γ \in (0, 1)$ , where $γ = 0$ corresponds to SQG…

math.AP2026

Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform $C^{1, \frac{4}{3} - 1 - ε}$ force

Diego Córdoba, Andrés Laín-Sanclemente, Luis Martínez-Zoroa

We establish the existence of solutions of the 2D incompressible non-homogeneous Euler equations with $C_{t}^{0} C_{x}^{1, \frac{4}{3} - 1 - ε} \cap C_{t}^{0} L_{x}^{2}$ …

math.AP2025

Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation

In-Jee Jeong, Luis Martínez-Zoroa, Wojciech S. Ożański

We prove instantaneous and continuous-in-time loss of supercritical Sobolev regularity for the 3D incompressible Euler equations in $R^{3}$ . Namely, for any $s \in (0, 3/2)$ …

math.AP2025

Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1, \frac{4}{3} - 1 - ε} \cap L^{2}$ force

Diego Córdoba, Andrés Laín-Sanclemente, Luis Martínez-Zoroa

We establish the existence of compactly supported solutions of the inviscid incompressible 2D Boussinesq equation with $C^{1, \frac{4}{3} - 1 - ε} \cap L^{2}$ force that…

math.AP2025

Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG

Diego Córdoba, José Lucas-Manchón, Luis Martínez-Zoroa

The general surface quasi-geostrophic equation is the scalar transport equation defined by \begin{equation*} \frac{\partial θ}{\partial t}+v^γ_1 \frac{\partial θ}{\partial x_1}+v^γ…

math.AP2024★ 1 cited

Non Existence and Strong Ill-Posedness in $H^{2}$ for the Stable IPM Equation

Roberta Bianchini, Diego Córdoba, Luis Martínez-Zoroa

We prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small $H^{2} (R^{2})$ perturbations of the linea…

math.AP2024★ 1 cited

Finite time singularities of smooth solutions for the 2D incompressible porous media (IPM) equation with a smooth source

Diego Córdoba, Luis Martínez-Zoroa

We establish the existence of smooth, finite-energy solutions to the 2D incompressible porous media equation (IPM), with a compactly supported uniformly smooth source, which develo…

math.AP2024★ 1 cited

Instantaneous continuous loss of regularity for the SQG equation

Diego Córdoba, Luis Martínez-Zoroa, Wojciech S. Ożański

Given $s \in (3/2, 2)$ and $ε > 0$ , we construct a compactly supported initial data $θ_{0}$ such that $∥ θ_{0} ∥_{H^{s}} \leq ε$ and there exist $T > 0$ , $c > 0$ and a loca…

math.AP2024

Finite time blow-up for the hypodissipative Navier Stokes equations with a force in $L_{t}^{1} C_{x}^{1, ε} \cap L_{t}^{\infty} L_{x}^{2}$

Diego Córdoba, Luis Martínez-Zoroa, Fan Zheng

In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is gi…

math.AP2023

Blow-up for the incompressible 3D-Euler equations with uniform $C^{1, \frac{1}{2} - ε} \cap L^{2}$ force

Diego Córdoba, Luis Martínez-Zoroa

This paper presents a novel approach to establish a blow-up mechanism for the forced 3D incompressible Euler equations, with a specific focus on non-axisymmetric solutions. We cons…

math.AP2023

Finite time singularities to the 3D incompressible Euler equations for solutions in $C^{\infty} (R^{3} ∖ {0}) \cap C^{1, α} \cap L^{2}$

Diego Córdoba, Luis Martínez-Zoroa, Fan Zheng

We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our…

math.AP2023

Global unique solutions with instantaneous loss of regularity for SQG with fractional diffusion

Diego Córdoba, Luis Martínez-Zoroa

In this work we construct global unique solutions of the dissipative Surface quasi-geostrophic equation ( $α$ -SQG) that lose regularity instantly when there is super-critical fracti…

math.AP2022

Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations

Diego Córdoba, Luis Martínez-Zoroa, Wojciech Ożański

We construct solutions of the 2D incompressible Euler equations in $\mathds{R}^2\times [0,\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^{β}$ for…

math.AP2022

Non-existence and strong ill-posedness in $C^{k, β}$ for the generalized Surface Quasi-geostrophic equation

Diego Córdoba, Luis Martínez-Zoroa

We consider solutions to the generalized Surface Quasi-geostrophic equation ( $γ$ -SQG) when the velocity is more singular than the active scalar function (i.e. $γ \in (0, 1)$ ). In this…

math.AP2021

Non existence and strong ill-posedness in $C^{k}$ and Sobolev spaces for SQG

Diego Córdoba, Luis Martínez-Zoroa

We construct solutions in $R^{2}$ with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in $C^{k}$ ( $k \geq 2$ ) but that are not in $C^{k}$ for…

Non Existence of the Stable 2D Boussinesq Equations in H2 via Density-Vorticity Feedback

Blow-up at finite time for the generalized SQG equations in the Sobolev well-posedness regime

Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform C1,34​​−1−ε force

Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation

Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform C1,34​​−1−ε∩L2 force

Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG

Non Existence and Strong Ill-Posedness in H2 for the Stable IPM Equation

Finite time singularities of smooth solutions for the 2D incompressible porous media (IPM) equation with a smooth source

Instantaneous continuous loss of regularity for the SQG equation

Finite time blow-up for the hypodissipative Navier Stokes equations with a force in Lt1​Cx1,ε​∩Lt∞​Lx2​

Blow-up for the incompressible 3D-Euler equations with uniform C1,21​−ε∩L2 force

Finite time singularities to the 3D incompressible Euler equations for solutions in C∞(R3∖{0})∩C1,α∩L2

Global unique solutions with instantaneous loss of regularity for SQG with fractional diffusion

Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations

Non-existence and strong ill-posedness in Ck,β for the generalized Surface Quasi-geostrophic equation

Non existence and strong ill-posedness in Ck and Sobolev spaces for SQG

Non Existence of the Stable 2D Boussinesq Equations in $H^{2}$ via Density-Vorticity Feedback

Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform $C^{1, \frac{4}{3} - 1 - ε}$ force

Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1, \frac{4}{3} - 1 - ε} \cap L^{2}$ force

Non Existence and Strong Ill-Posedness in $H^{2}$ for the Stable IPM Equation

Finite time blow-up for the hypodissipative Navier Stokes equations with a force in $L_{t}^{1} C_{x}^{1, ε} \cap L_{t}^{\infty} L_{x}^{2}$

Blow-up for the incompressible 3D-Euler equations with uniform $C^{1, \frac{1}{2} - ε} \cap L^{2}$ force

Finite time singularities to the 3D incompressible Euler equations for solutions in $C^{\infty} (R^{3} ∖ {0}) \cap C^{1, α} \cap L^{2}$

Non-existence and strong ill-posedness in $C^{k, β}$ for the generalized Surface Quasi-geostrophic equation

Non existence and strong ill-posedness in $C^{k}$ and Sobolev spaces for SQG