Related papers: Stability of a one-dimensional full viscous quantu…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
We investigate the non-uniqueness of weak solutions of the Quantum-Hydrodynamic system. This form of ill-posedness is related to the change of the number of connected components of the support of the position density (called nodal domains)…
In this paper we study time semi-discrete approximations of a class of polynomially stable infinite dimensional systems modeling the damped vibrations. We prove that adding a suitable numerical viscosity term in the numerical scheme, one…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
Fully resolved simulation of flows with buoyant particles is a challenging problem since buoyant particles are lighter than the surrounding fluid, and as a result, the two phases are strongly coupled together. In this work, the virtual…
Particles confined in droplets are called compound particles. They are encountered in various biological and soft matter systems. Hydrodynamics can play a decisive role in determining the configuration and stability of these multiphase…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
We study the existence and properties of the non-equilibrium steady state which arises by putting two copies of systems at different temperatures into a thermal contact. We solve the problem for the relativistic systems that are described…
The dynamics of quantum droplets in 1D is analyzed on the basis of the variational approach (VA). It is shown that the VA based on the super-Gaussian function gives a good approximation of stationary states. The period of small oscillations…
This paper is concerned with nonlinear stability of viscous contact discontinuity to inflow problem for the one-dimensional full compressible Navier-Stokes equations with different ends in half space $[0,\infty)$. For the case when the…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…