Related papers: Finite-Energy Weak Solutions to the Quantum Isothe…
We give an elementary proof for the interior double H\"{o}lder regularity of the hydrodynamic pressure for weak solutions of the Euler Equations in a bounded $C^2$-domain $\Omega \subset \mathbb{R}^d$; $d\geq 3$. That is, for velocity $u…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We consider the 3D Euler equations for incompressible homogeneous fluids and we study the problem of energy conservation for weak solutions in the space-periodic case. First, we prove the energy conservation for a full scale of Besov…
In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…
We are concerned with the existence of solutions to the following nonlinear Schr\"odinger system in $\mathbb{R}^3$: \begin{equation*} \left\{ \begin{aligned} -\Delta u_1 + (x_1^2+x_2^2)u_1&= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta…
We prove the existence of weak solutions in the space of energy for a class of non-linear Schroedinger equations in the presence of a external rough magnetic potential. Under our assumptions it is not possible to study the problem by means…
We study the stochastically forced system of isentropic Euler equations of gas dynamics with a $\gamma$-law for the pressure. We show the existence of martingale weak entropy solutions; we also discuss the existence and characterization of…
In this paper, we continue the analysis of the effective model of quantum Schwarzschild black holes recently proposed by some of the authors in [1,2]. In the resulting spacetime the central singularity is resolved by a black-to-white hole…
In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary effects. Formal a priori estimates show that the density of solutions to these systems should disperse…
In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…
We revisit the analogy suggested by Madelung between a non-relativistic time-dependent quantum particle, to a fluid system which is pseudo-barotropic, irrotational and inviscid. We first discuss the hydrodynamical properties of the Madelung…
In this paper, we are concerned with the hydrodynamic limit to rarefaction waves of the compressible Euler system for the Landau equation with Coulomb potentials as the Knudsen number $\epsilon>0$ is vanishing. Precisely, whenever…
We propose a generalization of quantum mechanical equations in the hydrodynamic form by introducing, into the Lagrangian density, terms taking into account the diffusion velocity at zero and finite temperatures and the diffusion pressure…
We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck equation coupled with the compressible isentropic Navier-Stokes system through a drag force…
In [Commun Math Phys 348(1), 129-143, 2016], Cheskidov et al. proved that physically realizable weak solutions of the incompressible 2D Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions are those that…