Diego Chamorro
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Global mild solutions in a critical setting for a forced fractional Boussinesq system Open
We study here mild solutions for the forced, incompressible fractional Boussinesq system. Under suitable estimates for the terms involved (in an adapted functional framework) we can invoque a fixed point argument in order to obtain mild so…
Liouville-type theorems for stationary Navier–Stokes equations with Lebesgue spaces of variable exponent Open
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 under some additional information over the velocity field, w…
New weighted Riesz-type pointwise inequalities and applications to generalized Sobolev estimates Open
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of w…
Some general external forces and critical mild solutions for the fractional Navier–Stokes equations Open
In this article we study mild solutions for the forced, incompressible fractional Navier–Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the non…
The Role of the Dimension in Uniqueness Results for the Fractional Stationary Quasi‐Geostrophic System Open
In this paper, we study a Liouville‐type theorem for the stationary fractional quasi‐geostrophic equation in various dimensions. Indeed, our analysis focuses essentially on dimensions , and we explore the uniqueness of weak solutions for t…
Some general external forces and critical mild solutions for the fractional Navier-Stokes equations Open
In this article we study mild solutions for the forced, incompressible fractional Navier-Stokes equations. These solutions are classically obtained via a fixed-point argument which relies on suitable estimates for the initial data, the non…
Global weak solutions for a variation of the Whitham equation Open
We study in this article a variation of the Whitham equation which was introduced as an alternative to the KdV equation. We first prove the global existence of weak solutions, then we establish a regularity criterion from which we deduce t…
Partial suitable solutions for the micropolar equations and regularity properties Open
The incompressible Micropolar system is given by two coupled equations: the first equation gives the evolution of the velocity field while the second equation gives the evolution of the microrotation field . In this article we will conside…
The role of the dimension in uniqueness results for the stationary quasi-geostrophic system Open
In this paper, we study a Liouville-type theorem for the stationary fractional quasi-geostrophic equation in various dimensions. Indeed, our analysis focuses on dimensions n = 2, 3, 4 and we explore the uniqueness of weak solutions for thi…
Partial regularity and $L^3$-norm concentration effects around possible blow-up points for the micropolar fluid equations Open
The micropolar fluid system is a model based on the Navier-Stokes equations which considers two coupled variables: the velocity field $\vec u$ and the microrotation field $\vecω$. Assuming an additional condition over the variable $\vec u$…
Liouville type theorems for stationary Navier-Stokes equations with Lebesgue spaces of variable exponent Open
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 under some additional information over the velocity field, w…
Lebesgue spaces with variable exponent: some applications to the Navier-Stokes equations Open
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 spaces present some particularities that make them quite diffe…
A turbulent study for a damped Navier-Stokes equation: turbulence and problems Open
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and w…
A new approach for the regularity of weak solutions of the 3D Boussinesq system Open
We address here the problem of regularity for weak solutions of the 3D Boussinesq equation. By introducing the new notion of partial suitable solutions, which imposes some conditions over the velocity field only, we show a local gain of re…
Partial suitable solutions for the micropolar equations and regularity properties Open
The incompressible Micropolar system is given by two coupled equations: the first equation gives the evolution of the velocity field u while the second equation gives the evolution of the microrotation field $ω$. In this article we will co…
On an almost sharp Liouville type theorem for fractional Navier-Stokes equations Open
We investigate existence, Liouville type theorems and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power $(-Δ)^{\fracα{2}}…
Non Linear Singular Drifts and Fractional Operators Open
We consider parabolic PDEs associated with fractional type operators drifted by non-linear singular first order terms. When the drift enjoys some boundedness properties in appropriate Lebesgue and Besov spaces, we establish by exploiting a…
A crypto-regularity result for the micropolar fluids equations Open
In the analysis of PDEs, regularity of often measured in terms of Sobolev, H{ö}lder, Besov or Lipschitz spaces, etc. However, sometimes a gain of regularity can also be expressed just in terms of Lebesgue spaces, by passing from a singular…
Some existence and regularity results for a non-local transport-diffusion equation with fractional derivatives in time and space Open
We study the existence of global weak solutions of a nonlinear transport-diffusion equation with a fractional derivative in the time variable and under some extra hypotheses, we also study some regularity properties for this type of soluti…
Interior epsilon-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term Open
We develop here a particular version of the partial regularity theory for the Magneto-Micropolar equations (MMP) where a perturbation term is added. These equations are used in some special cases, such as in the study of the evolution of l…
Mixed Sobolev-like Inequalities in Lebesgue spaces of variable exponents and in Orlicz spaces Open
In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of vari…