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Diego Cordoba

Publications and source records attributed to Diego Cordoba.

At least 19 recordsLinked to original sources
arXiv2024

Modeling the crust and upper mantle in northern Beata Ridge (CARIBE NORTE Project)

The complex tectonic region of NE Caribbean, where Hispaniola and Puerto Rico are located, is bordered by subduction zone with oblique convergence in the north and by incipient subduction zone associated to Muertos Trough in the south. Central Caribbean basin is characterized by the presence of a prominent topographic structure known as Beata Ridge, whose oceanic crustal thickness is unusual. The northern part of Beata Ridge is colliding with the central part of Hispaniola along a transverse NE alignment, which constitutes a morphostructural limit, thus producing the interruption of the Cibao Valley and the divergence of the rivers and basins in opposite directions. The direction of this alignment coincides with the discontinuity that could explain the extreme difference between west and east seismicity of the island. Different studies have provided information about Beata Ridge, mainly about the shallow structure from MCS data. In this work, CARIBE NORTE (2009) wide-angle seismic data are analyzed along a WNW-ESE trending line in the northern flank of Beata Ridge, providing a complete tectonic view about shallow, middle and deep structures. The results show clear tectonic differences between west and east separated by Beata Island. In the Haiti Basin area, sedimentary cover is strongly influenced by the bathymetry and its thickness decreases toward to the island. In this area, the Upper Mantle reaches 20 km deep increasing up to 24 km below the island where the sedimentary cover disappears.

physics.geo-ph↗
arXiv2024

Seismic structure of the crust in the western Dominican Republic

The contact between the Caribbean and North American plates is a tectonically complicated boundary where the deformation is accommodated in north and south of Hispaniola by the Enriquillo Plantain Garden and Septentrional Oriente Fault Zones. We present a crustal and tectonic study of the Northeastern Caribbean Plate Boundary from wide-angle seismic data acquired during the GEOPRICO-DO and CARIBE NORTE surveys, showing two transects crossing, from north to south, North American Plate, Bahamas Platform, central Hispaniola and Caribbean Plate. The results presented include two 2D P wave velocity models of 425 km and 200 km long oriented NNE SSW and ENE SSW, respectively, obtained by the travel time forward and inverse modeling of the WAS data. Our study defines that the contact between Bahamas Platform, North American Plate and Hispaniola corresponds to oblique subduction with the Moho dipping 11 in the NNE SSW direction. Furthermore, in the south, our results reveal the existence of an anomalous deep-reaching zone of lateral velocity variation in the mantle that could be associated with EPGFZ and a possible detached oceanic slab from NOAM that could explain the deep seismicity in the region.

physics.geo-ph↗
arXiv2024

Morphotectonic Study of the Greater Antilles

The first morphotectonic model of the Greater Antilles is presented. The model is adjusted to the current dynamics between the Caribbean and North American plates. It is mainly elaborated by Rantsmans methodology. We determined 2 megablocks, 7 macroblocks, 42 mesoblocks, 653 microblocks and 1264 nanoblocks. They constitute a set of active blocks under rotation, uplifting and tilting movements. A total of 11 active knots of faults and 8 cells are the main articulation areas. The largest seismogenetic structures in the Northern Caribbean are an array of the active fault segments. The majority of them are in the Caribbean-North American Plate Boundary Zone, the Hispaniola has the most complex neotectonic structure associated with the central axis of the morphotectonic deformations in the region.

physics.geo-ph↗
arXiv2023

Finite-time singularity formation for angled-crested water waves

We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a corner, it remains a corner but generically its angle changes. Using a characterization of the asymptotic behavior of the fluid near a corner that follows from our a priori energy estimates, we show the existence of initial data in these spaces for which the fluid becomes singular in finite time.

math.AP↗
arXiv2021

Self-intersecting interfaces for stationary solutions of the two-fluid Euler equations

We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly with a small gravity constant, that feature a splash singularity. More precisely, in the solutions we construct the interface is a $C^{2,α}$ smooth curve that intersects itself at one point, and the vorticity density on the interface is of class $C^α$. The proof consists in perturbing Crapper's family of formal stationary solutions with one fluid, so the crux is to introduce a small but positive second-fluid density. To do so, we use a novel set of weighted estimates for self-intersecting interfaces that squeeze an incompressible fluid. These estimates will also be applied to interface evolution problems in a forthcoming paper.

math.AP↗
arXiv2020

Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$

We prove a global existence result of a unique strong solution in $\dot H^{5/2} \cap \dot H^{3/2}$ with small $\dot H^{3/2}$ semi-norm for the 2D Muskat problem, hence allowing the interface to have arbitrary large finite slopes and finite energy (thanks to the $L^{2}$ maximum principle). The proof is based on the use of a new formulation of the Muskat equation that involves oscillatory terms. Then, a careful use of interpolation inequalities in homogeneneous Besov spaces allows us to close the {\emph{a priori}} estimates.

math.AP↗
arXiv2015

Splash singularities for the one-phase Muskat problem in stable regimes

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we found is with a dry region, where the density and the viscosity are set equal to $0$ (the gradient of the pressure is equal to $(0,0)$) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.

math.AP↗
arXiv2014

On the Muskat problem: global in time results in 2D and 3D

This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an $L^2$ maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the estimates from our paper \cite{PDPB} to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in critical spaces, giving solutions with bounded slope and time integrable bounded curvature.

math.AP↗
arXiv2013

Local solvability and turning for the inhomogeneous Muskat problem

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane $\mathbb{R}^2$ or a bounded strip $S=\mathbb{R}\times(-π/2,π/2)$. The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in \cite{ccfgl} for the homogeneus Muskat problem with infinite depth.

math.AP↗
arXiv2012

Breakdown of smoothness for the Muskat problem

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 $C^4$.

math.AP↗
arXiv2011

Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.

math.AP↗
arXiv2010

Turning waves and breakdown for incompressible flows

We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by $(\al,f_0(\al))$, the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time $t^*$ where the solution of the free boundary problem parameterized as $(\al,f(\al,t))$ blows-up: $\|\da f\|_{L^\infty}(t^*)=\infty$. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.

math.AP↗
arXiv2010

On the global existence for the Muskat problem

The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new ``log'' conservation law \eqref{ln} which is satisfied by the equation \eqref{ec1d} for the interface. Our second result is a proof of global existence of Lipschitz continuous solutions for initial data that satisfy $\|f_0\|_{L^\infty}<\infty$ and $\|\partial_x f_0\|_{L^\infty}<1$. We take advantage of the fact that the bound $\|\partial_x f_0\|_{L^\infty}<1$ is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law. Lastly, we prove a global existence result for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance $\| f\|_1 \le 1/5$. Previous results of this sort used a small constant $ε\ll1$ which was not explicit.

math.AP↗
arXiv2010

A naive parametrization for the vortex-sheet problem

We consider the dynamics of a vortex sheet that evolves by the Birkhoff-Rott equations. The fluid evolution is understood as a weak solution of the incompressible Euler equations where the vorticity is given by a delta function on a curve multiplied by an amplitude. The solutions we study are with finite energy, which implies zero mean amplitude. In this context we choose a parametrization for the motion of the vortex sheet for which the equation is well-posed for analytic initial data. For the equation of the amplitude we show ill-posedness for non-analytic initial data.

math.AP↗
arXiv2010

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the Rayleigh-Taylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.

math.AP↗
arXiv2010

Singularity Formation in a Surface Wave Model

In this paper we study the Burgers equation with a nonlocal term of the form $Hu$ where $H$ is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch. We prove blow up in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form $Λ^αHu$ for $0<α< 1$, finite time singularity formation is also shown.

math.AP↗
arXiv2009

Absence of squirt singularities for the multi-phase Muskat problem

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.

math.AP↗