Daniel Marroquin
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View article: On Hodge Decomposition, Effective Viscous Flux and Compressible Navier-Stokes
On Hodge Decomposition, Effective Viscous Flux and Compressible Navier-Stokes Open
It has been known, since the pioneering works by Serre, Hoff, Vaȋgant-Kazhikhov, Lions and Feireisl, among others, the regularizing properties of the effective viscous flux and its characterization as the function whose gradient is the gra…
View article: Global weak solutions for the compressible Poisson-Nernst-Planck-Navier-Stokes System
Global weak solutions for the compressible Poisson-Nernst-Planck-Navier-Stokes System Open
We consider the compressible Poisson-Nernst-Planck-Navier-Stokes (PNPNS) system of equations, governing the transport of charged particles under the influence of the self-consistent electrostatic potential, in a three-dimensional bounded d…
View article: Invariant measures for stochastic parabolic-hyperbolic equations in the space of almost periodic functions: Lipschitz flux case
Invariant measures for stochastic parabolic-hyperbolic equations in the space of almost periodic functions: Lipschitz flux case Open
We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity func…
View article: Invariant measures for stochastic conservation laws with Lipschitz flux in the space of almost periodic functions
Invariant measures for stochastic conservation laws with Lipschitz flux in the space of almost periodic functions Open
We study the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the exis…
View article: Homogenization of stochastic conservation laws with multiplicative noise
Homogenization of stochastic conservation laws with multiplicative noise Open
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the…
View article: A Boundary Value Problem for a Class of Anisotropic Stochastic Degenerate Parabolic-Hyperbolic Equations
A Boundary Value Problem for a Class of Anisotropic Stochastic Degenerate Parabolic-Hyperbolic Equations Open
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain $\cO=\cO'\X\cO''$ where a Neumann boundary condition is imposed on $\po\cO'\X\cO"…
View article: The Dirichlet Problem for Stochastic Degenerate Parabolic-Hyperbolic Equations
The Dirichlet Problem for Stochastic Degenerate Parabolic-Hyperbolic Equations Open
We consider the Dirichlet problem for a quasilinear degenerate parabolic stochastic partial differential equation with multiplicative noise and nonhomogeneous Dirichlet boundary condition.We introduce the definition of kinetic solution for…
View article: Global Smooth Solutions With Large Data for a System Modeling Aurora Type Phenomena in the 2-Torus
Global Smooth Solutions With Large Data for a System Modeling Aurora Type Phenomena in the 2-Torus Open
We prove existence and uniqueness of smooth solutions with large initial data for a system of equations modeling the interaction of short waves, governed by a nonlinear Schrödinger equation, and long waves, described by the equations of ma…
View article: On Hodge decomposition, effective viscous flux and compressible Navier-Stokes
On Hodge decomposition, effective viscous flux and compressible Navier-Stokes Open
It has been known, since the pioneering works by Serre, Hoff, Vaĭgant-Kazhikhov, Lions and Feireisl, among others, the regularizing properties of the effective viscous flux and its characterization as the function whose gradient is the gra…
View article: On the generalized almost periodic homogenization of stochastic conservation laws with multiplicative noise
On the generalized almost periodic homogenization of stochastic conservation laws with multiplicative noise Open
We consider the generalized almost periodic homogenization problem for two types of stochastic conservation laws with oscillatory coefficients and a multiplicative noise, namely, the nonlinear transport equation and the equation with a sti…
View article: Homogenization of Stochastic Conservation Laws with Multiplicative Noise
Homogenization of Stochastic Conservation Laws with Multiplicative Noise Open
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the…
View article: The Strong Trace Property and the Neumann Problem for Stochastic Conservation Laws
The Strong Trace Property and the Neumann Problem for Stochastic Conservation Laws Open
We establish the well-posedness of the Neumann problem for stochastic conservation laws with multiplicative noise. As a major step for establishing the uniqueness of the kinetic solution to the referred problem we establish the new strong …
View article: Global smooth solutions with large data for a system modeling aurora\n type phenomena in the 2-torus
Global smooth solutions with large data for a system modeling aurora\n type phenomena in the 2-torus Open
We prove existence and uniqueness of smooth solutions with large initial data\nfor a system of equations modeling the interaction of short waves, governed by\na nonlinear Schr\\"odinger equation, and long waves, described by the equations\…
View article: Short Wave-Long Wave Interactions in planar Magnetohydrodynamics
Short Wave-Long Wave Interactions in planar Magnetohydrodynamics Open
We study several mathematical aspects of a system of equations modelling the interaction between short waves, described by a nonlinear Schr\{o}dinger equation, and long waves, described by the equations of magnetohydrodynamics (MHD) for a …