Related papers: Existence and weak-strong uniqueness for damage sy…
Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular…
In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…
In a previous work [8], it was shown that the joint law of a diffusion process and the running supremum of its first component is absolutely continuous, and that its density satisfies a non standard weak partial differential equation (PDE).…
The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…
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…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…
We prove an analog of the Caffarelli-Kohn-Nirenberg theorem for weak solutions of a system of PDE that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of…
We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for…
In this work, we present a result on the local existence and uniqueness of solutions to nonlinear Partial Differential-Algebraic Equations (PDAEs). By applying established theoretical results, we identify the conditions that guarantee the…
We consider a coupled system of partial and ordinary differential equations describing the interaction between an isentropic inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions…
This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…
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…
The purpose of this paper is to study the existence and uniqueness of solutions to a Stochastic Differential Equation (SDE) coming from the eigenvalues of Wishart processes. The coordinates are non-negative, evolve as Cox-Ingersoll-Ross…
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)…