Gastón Vergara-Hermosilla

Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations

Albert Ai, Gaston Vergara-Hermosilla

We establish Liouville-type theorems for the three-dimensional stationary fractional magnetohydrodynamic (MHD) system with different orders of dissipation. Our first result shows t…

Remarks on a Liouville-type theorem by Chae and Wolf for stationary Navier-Stokes equations

Raúl Fierro, Gaston Vergara-Hermosilla

In this note, we revisit a Liouville-type theorem of Chae and Wolf for stationary Navier-Stokes equations in $R^{3}$ [J. Differential Equations 261 (2016) 5541-5560]. We sho…

Liouville Theorems Above the Critical $9/2$ Threshold for Stationary Navier-Stokes Equations

Gaston Vergara-Hermosilla

We establish new Liouville-type theorems for the stationary Navier-Stokes equations in $R^{3}$ . A central open problem in this context is whether the classical $L^{9/2}(\mat…

Notes on Liouville-type theorems for the 3D stationary Navier-Stokes equations

Hongling Jiang, Jianfeng Sun, Gastón Vergara-Hermosilla +1

In \cite{CV23}, Chamorro and Vergara-Hermosilla established several Liouville-type theorems to the Navier-Stokes equations in the framework of the variable Lebesgue spaces. These r…

Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component

Gaston Vergara-Hermosilla

We study Liouville-type results for the stationary Navier--Stokes equations in $R^{3}$ . We prove that any $H ˙^{1} (R^{3})$ solution is trivial under an integrabilit…

math.AP2025

Finite time blow-up for a nonlinear parabolic equation with smooth coefficients

Oscar Jarrin, Gaston Vergara-Hermosilla

In this article, we consider an n-dimensional parabolic partial differential equation with a smooth coefficient term in the nonlinear gradient term. This equation was first introdu…

Global well-posedness of the Navier--Stokes equations and the Keller--Segel system in variable Fourier--Besov spaces

Gastón Vergara-Hermosilla, Jihong Zhao

In this paper, we study the Cauchy problem of the classical incompressible Navier--Stokes equations and the parabolic-elliptic Keller--Segel system in the framework of the Fourier-…

Global well-posedness of the fractional dissipative system in the framework of variable Fourier--Besov spaces

Gastón Vergara-Hermosilla, Jihong Zhao

In this paper, we are concerned with the well-posed issues of the fractional dissipative system in the framework of the Fourier--Besov spaces with variable regularity and integrabi…

Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations

Kai Koike, Franck Sueur, Gastón Vergara-Hermosilla

We consider a viscous compressible barotropic flow in the interval $[0, π]$ with homogeneous Dirichlet boundary conditions for the flow velocity and a constant rest state as initial…

On the Cauchy problem for the fractional Keller-Segel system in variable Lebesgue spaces

Gastón Vergara-Hermosilla, Jihong Zhao

In this paper, we are mainly concerned with the well-posed problem of the fractional Keller--Segel system in the framework of variable Lebesgue spaces. Based on carefully examining…

Well-posedness of the 2D surface quasi-geostrophic equation in variable Lebesgue spaces

Hao Chen, Gastón Vergara-Hermosilla, Jihong Zhao

In this paper, we are mainly concerned with the well-posedness of the dissipative surface quasi-geostrophic equation in the framework of variable Lebesgue spaces. Based on some ana…

On variable Lebesgue spaces and generalized nonlinear heat equations

Gastón Vergara-Hermosilla

In this work we address some questions concerning the Cauchy problem for a generalized nonlinear heat equations considering as functional framework the variable Lebesgue spaces $L^…

On the blow-up for a Kuramoto-Velarde type equation

Oscar Jarrin, Gaston Vergara-Hermosilla

It is known that the Kuramoto-Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters $γ_{1}$ and $γ_{2}$ involved in the non-linear terms verify $ γ_…

Remarks on variable Lebesgue spaces and fractional Navier-Stokes equations

Gastón Vergara-Hermosilla

In this work we study the 3D Navier-Stokes equations, under the action of an external force and with the fractional Laplacian operator $(- Δ)^{α}$ in the diffusion term, from the poin…

Liouville type theorems for stationary Navier-Stokes equations with Lebesgue spaces of variable exponent

Diego Chamorro, Gastón Vergara-Hermosilla

In this article we study some Liouville-type theorems for the stationary 3D Navier-Stokes equations. These results are related to the uniqueness of weak solutions for this system u…

An Lp-theory for fractional stationary Navier-Stokes equations

Oscar Jarrín, Gastón Vergara-Hermosilla

We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian opera…

Lebesgue spaces with variable exponent: some applications to the Navier-Stokes equations

Diego Chamorro, Gastón Vergara-Hermosilla

In this article we study some problems related to the incompressible 3D Navier-Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spa…