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In this paper, we consider a two-phase flow model consisting of the compressible Navier-Stokes systems with degenerate viscosity coupled with the compressible Navier-Stokes systems with constant viscosities via a drag force, which can be…

Analysis of PDEs · Mathematics 2022-03-11 Ya-Ting Wang , Ling-Yun Shou

We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…

Analysis of PDEs · Mathematics 2024-01-02 Oscar Jarrin

We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…

Analysis of PDEs · Mathematics 2017-12-06 Peter Constantin , Vlad Vicol

In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution schemes are fulfilling the underlying structure preserving…

Numerical Analysis · Mathematics 2022-12-06 Rémi Abgrall , Mária Lukácova-Medvid'ová , Philipp Öffner

In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations as a differential…

Analysis of PDEs · Mathematics 2011-05-06 Camillo De Lellis , László Székelyhidi

The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…

Dynamical Systems · Mathematics 2025-11-07 Irena Lasiecka , Vando Narciso

This work concerns the global existence of the weak solutions to a system of partial differential equations modeling the evolution of particles in the fluid. That system is given by a coupling between the standard isentropic compressible…

Analysis of PDEs · Mathematics 2018-06-13 Irene M. Gamba , Cheng Yu

The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…

Analysis of PDEs · Mathematics 2016-01-19 Jacek Cyranka , Piotr B Mucha , Edriss S Titi , Piotr Zgliczyński

We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the…

Analysis of PDEs · Mathematics 2021-07-28 Pedro Gabriel Fernández-Dalgo , Pierre Gilles Lemarié-Rieusset

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law $p({\rho}) = {\rho}^2$ and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are…

Analysis of PDEs · Mathematics 2014-08-26 Elisabetta Chiodaroli , Camillo De Lellis , Ondrej Kreml

We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The vacuum regions are included in the weak formulation of the…

Analysis of PDEs · Mathematics 2022-08-02 Paolo Antonelli , Lars Eric Hientzsch , Stefano Spirito

The pressureless Euler-Navier-Stokes system can be obtained formally from the Vlasov-Navier-Stokes system, under the assumption that the distribution function describing the density of particles is monokinetic. Its study has been the…

Analysis of PDEs · Mathematics 2026-02-09 Raphaël Danchin

We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…

Mathematical Physics · Physics 2023-04-19 Dirk Hennig

In this paper, we consider global weak solutions to com-pressible Navier-Stokes-Korteweg equations with density dependent viscosities , in a periodic domain $\Omega = \mathbb T^3$, with a linear drag term with respect to the velocity. The…

Analysis of PDEs · Mathematics 2020-07-22 Didier Bresch , Marguerite Gisclon , Ingrid Lacroix-Violet , Alexis Vasseur

Consider a random initial vorticity $\omega_0(x) = \sum_{n\in \mathbb{Z}^2} a_n \phi(x-n)$, where $\phi$ is bounded and compactly supported and $\{a_n\}$ are independent, uniformly bounded, mean $0$, variance $1$ random variables (i.e.…

Analysis of PDEs · Mathematics 2025-12-09 Gautam Iyer , Milton C. Lopes Filho , Helena J. Nussenzveig Lopes

We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.

Analysis of PDEs · Mathematics 2017-09-04 Diego Chamorro , Pierre Gilles Lemarié-Rieusset , Kawther Mayoufi

We consider the 2-d isentropic compressible Euler equations. It was shown in by E. Chiodaroli, C. De Lellis and O. Kreml that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak…

Analysis of PDEs · Mathematics 2019-01-21 Simon Markfelder , Christian Klingenberg

We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$.…

Probability · Mathematics 2020-04-22 Hakima Bessaih , Benedetta Ferrario

We study the infinite-energy solutions of the Cahn-Hilliard equation in the whole 3D space in uniformly local phase spaces. In particular, we establish the global existence of solutions for the case of regular potentials of arbitrary…

Analysis of PDEs · Mathematics 2012-05-08 Jon Pennant , Sergey Zelik

We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…

Analysis of PDEs · Mathematics 2009-03-20 Uwe Brauer , Lavi Karp