Author profile: Gancedo García, Francisco
Institutional data
Name | Gancedo García, Francisco |
Department | Análisis Matemático |
Knowledge area | Análisis Matemático |
Professional category | Profesor Titular de Universidad |
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Statistics
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No. publications
41
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No. visits
6193
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No. downloads
9640
Publications |
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PhD Thesis
Free boundary and turbulence for incompressible viscous fluids
(2023)
The mathematical bases of the dynamics of viscous fluids are given by the classical Navier- Stokes equations, which model ... |
Final Degree Project
Solutions for the Surface Quasigeostrophic equation
(2023)
The main aim of this project is to understand the surface quasi-geostrophic model (SQG) and prove the existence of global ... |
Article
Quantitative Hölder estimates for even singular integral operators on patches
(ScienceDirect, 2022)
In this paper we show a constructive method to obtain estimates of even singular integral operators on characteristic ... |
Final Degree Project
Deducción y resolución de las ecuaciones de las olas del mar lineales
(2022)
The main goal of this work is to prove the existence and uniqueness of solutions to the water waves equation in 2-D. We ... |
Article
Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
(ScienceDirect, 2020)
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. ... |
PhD Thesis
Global regularity for incompressible fluid interfaces.
(2018)
Esta memoria esta dedicada al estudio de tres problemas de frontera libre dadas por interfases entre fluidos incompresibles: ... |
Final Degree Project
Soluciones débiles en mecánica de fluidos
(2018)
The main aim of this work is to prove theoretical results on partial differential equations from fluid mechanics. Particularly, ... |
Article
Uniqueness for SQG patch solutions
(American Mathematical Society, 2018)
This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence ... |
Article
Global regularity of 2D density patches for inhomogeneous Navier-Stokes
(Springer, 2018)
This paper is about Lions’ open problem on density patches: whether inhomogeneous incompressible Navier-Stokes equations ... |
Final Degree Project
Soluciones explícitas de las ecuaciones de los fluidos y consecuencias
(2017)
Entender el movimiento de los líquidos, gases y plasmas forma la parte central de la Mecánica de Fluidos, que es de gran ... |
Article
A survey for the Muskat problem and a new estimate
(Springer, 2017)
This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which ... |
Article
On the Muskat problem: global in time results in 2D and 3D
(Johns Hopkins University Press, 2016)
This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides ... |
Article
Splash singularities for the one-phase Muskat problem in stable regimes
(Springer, 2016)
This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is ... |
Article
Structural stability for the splash singularities of the water waves problem
(American Institute of Mathematical Sciences, 2014)
In this paper we show a structural stability result for water waves. The main motivation for this result is that we would ... |
Article
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
(National Academy of Sciences (United States), 2014)
In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the “splash ... |
Article
Breakdown of smoothness for the Muskat problem
(Springer, 2013)
In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, i.e., no longer belongs to C4. |
Article
On the global existence for the Muskat problem
(European Mathematical Society, 2013)
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant ... |
Article
Porous media: the Muskat problem in 3D
(Mathematical Sciences Publishers, 2013)
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall ... |
Article
2º Congreso de Jóvenes Investigadores
(Real Sociedad Matematica Española, 2013)
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Article
Finite time singularities for the free boundary incompressible Euler equations
(Princeton University, 2013)
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also ... |
Article
On a singular incompressible porous media equation
(AIP Publishing, 2012)
This paper considers a family of active scalar equations with transport velocities which are more singular by a derivative ... |
Article
Finite time singularities for water waves with surface tension
(AIP Publishing, 2012)
Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension ... |
Article
Splash singularity for water waves
(National Academy of Sciences, 2012)
We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the ... |
Article
Generalized surface quasi-geostrophic equations with singular velocities
(Wiley, 2012)
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity ... |
Article
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
(Princeton University, 2012)
The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor ... |
Article
Lack of uniqueness for weak solutions of the incompressible porous media equation
(Springer, 2011)
In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz´ekelyhidi we prove non-uniqueness for solutions in L∞ in space and time. |
Article
Turning waves and breakdown for incompressible flows
(National Academy of Sciences, 2011)
We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. ... |
Article
Interface evolution: the Hele-Shaw and Muskat problems
(Princeton University, 2011)
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from ... |
Article
Singularity formations for a surface wave model
(IOP Publishing, 2010)
In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This ... |
Article
Absence of squirt singularities for the multi-phase Muskat problem
(Springer, 2010)
In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical ... |
Article
Interface evolution: water waves in 2-D
(Elsevier, 2010)
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface ... |
Article
Some recent results on the Muskat problem
(Cellule MathDoc, 2010)
We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by ... |
Presentation |
Article
Incompressible flow in porous media with fractional diffusion
(IOP Publishing, 2009)
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous ... |
Article
The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
(National Academy of Sciences, 2009)
For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible ... |
Article
A maximum principle for the Muskat problem for fluids with different densities
(Springer, 2009)
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s ... |
Article
Contour dynamics for 2D active scalars
(European Mathematical Society, 2009)
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Article
A note on interface dynamics for convection in porous media
(Elsevier, 2008)
We study the fluid interface problem through porous media given by two incompressible 2-D fluids of different densities. ... |
Article
Existence for the α-patch model and the QG sharp front in Sobolev spaces
(Elsevier, 2008)
We consider a family of contour dynamics equations depending on a parameter α with 0<α⩽1. The vortex patch problem of the ... |
Article
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
(Springer, 2007)
We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which ... |
Article
Analytical behavior of two-dimensional incompressible flow in porous media
(AIP Publishing (American Institute of Physics), 2007)
In this paper we study the analytic structure of a two-dimensional mass balance equation of an incompressible fluid in a ... |