Related papers: A mode of convergence arising in diffusive relaxat…
We discuss different notions of continuous solutions to the balance law \[u_t + (f(u ))_x =g \] with $g$ bounded, $f\in C^{2}$, extending previous works relative to the flux $f(u)=u^{2}$. We establish the equivalence among distributional…
Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…
Let $\mathcal{S} = \{ \tau_n \}_{n=1}^\infty \subset (0,T)$ be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
Numerical approximation of a general class of nonlinear unidirectional wave equations with a convolution-type nonlocality in space is considered. A semi-discrete numerical method based on both a uniform space discretization and the discrete…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex…
Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small…
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…
The underlying theme of this article is a class of sequences in metric structures satisfying a much weaker kind of Cauchy condition, namely quasi-Cauchy sequences (introduced in \cite{bc}) that has been used to define several new concepts…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to…
A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in…
In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…
We study the one-dimensional isentropic compressible Euler equations with linear (frictional) damping, subject to multiplicative, white-in-time stochastic forcing. The system is posed on a bounded interval with $L^\infty$ initial data and…
This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions…
We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…
The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background radiation studies. Then it derives the exact solution in terms of a series expansion to a…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…