The mathematical bases of the dynamics of viscous fluids are given by the classical Navier- Stokes equations, which model ...

The main aim of this project is to understand the surface quasi-geostrophic model (SQG) and prove the existence of global ...

In this paper we show a constructive method to obtain estimates of even singular integral operators on characteristic ...

The main goal of this work is to prove the existence and uniqueness of solutions to the water waves equation in 2-D. We ...

This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. ...

Esta memoria esta dedicada al estudio de tres problemas de frontera libre dadas por interfases entre fluidos incompresibles: ...

The main aim of this work is to prove theoretical results on partial differential equations from fluid mechanics. Particularly, ...

This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence ...

This paper is about Lions’ open problem on density patches: whether inhomogeneous incompressible Navier-Stokes equations ...

Entender el movimiento de los líquidos, gases y plasmas forma la parte central de la Mecánica de Fluidos, que es de gran ...

This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which ...

This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides ...

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is ...

In this paper we show a structural stability result for water waves. The main motivation for this result is that we would ...

In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the “splash ...

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.

The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant ...

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall ...

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also ...

This paper considers a family of active scalar equations with transport velocities which are more singular by a derivative ...

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension ...

We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the ...

This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity ...

The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor ...

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.

We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. ...

We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from ...

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This ...

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical ...

We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface ...

We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by ...

In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous ...

For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible ...

We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s ...

We study the fluid interface problem through porous media given by two incompressible 2-D fluids of different densities. ...

We consider a family of contour dynamics equations depending on a parameter α with 0<α⩽1. The vortex patch problem of the ...

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which ...

In this paper we study the analytic structure of a two-dimensional mass balance equation of an incompressible fluid in a ...