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Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results…

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…

We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of…

We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

This paper is devoted to show a couple of typicality results for weak solutions $v\in C^\theta$ of the Euler equations, in the case $\theta<1/3$. It is known that convex integration schemes produce wild weak solutions that exhibit anomalous…

We consider a model of a viscoelastic compressible flow in $R^{3}$ which is additionally shear thickening (the stress tensor corresponds to the power law model, however, the divergence of the velocity is due to the model bounded). We prove…

We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity…

Typically, a stochastic model relates stochastic "inputs" and, perhaps, controls to stochastic "outputs". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of…

So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point…

The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…

For the $1$-d isothermal Euler system, we consider the family of entropic BV solutions with possibly large, but finite, total variation. We show that these solutions are stable with respect to large perturbations in a class of weak…

In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit…

We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…

In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning…

We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation…