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We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global…
To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant solutions. Even under the presence of infinitely many…
The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs…
We prove a priori estimates for the system of partial differential equations modeling the interaction between an elastic body and an incompressible fluid in a 3D curved domain. The fluid is governed by the incompressible Navier-Stokes…
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm…
An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to…
The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact…
The paper is devoted to investigating the well-posedness, stability and large-time behavior near the hydrostatic balance for the 2D Boussinesq equations with partial dissipation. More precisely, the global well-posedness is obtained in the…
We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($\mu$…
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…
This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain perturbation problem. We find that the stability holds when…
Reductions of the KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, are studied. Specifically, the…
A new stochastic control problem of a dam-reservoir system installed in a river is analyzed both mathematically and numerically. Water balance dynamics of the reservoir are piece-wise deterministic and are driven by a stochastic…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed…
Under the hydrodynamic equilibrium Buchdahl's conditions on the behavior of the density and the pressure, for regular fluid static circularly symmetric star in (2 + 1) dimensions in the presence of a cosmological constant, is established…