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We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time…

Analysis of PDEs · Mathematics 2019-08-09 Naoki Tsuge

By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of…

Analysis of PDEs · Mathematics 2024-07-29 Luigi De Rosa , Theodore D. Drivas , Marco Inversi

Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $\epsilon\rightarrow 0^+$. Using the Hilbert expansion, we rigorously…

Analysis of PDEs · Mathematics 2020-10-02 Lei Wu , Zhimeng Ouyang

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

Analysis of PDEs · Mathematics 2024-07-02 Timothée Crin-Barat , Yue-Jun Peng , Ling-Yun Shou , Jiang Xu

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

Analysis of PDEs · Mathematics 2013-05-07 Demetrios Christodoulou , Shuang Miao

We prove a global-in-time limit from the two-species Vlasov-Maxwell-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. Besides the techniques developed for the classical solutions to the…

Analysis of PDEs · Mathematics 2023-06-13 Ning Jiang , Yi-Long Luo , Teng-Fei Zhang

This paper is devoted to the study of the compressible boundary layer equations in the Gevrey-2 solution space. Compared to the classical Prandtl equation, the additional complexity arises from the strong interaction between viscous layer…

Analysis of PDEs · Mathematics 2026-04-20 Ya-Guang Wang , Yi-Lei Zhao

We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish local-in-time, for any time, Cauchy theories that are…

Mathematical Physics · Physics 2023-02-08 Marc Briant , Arnaud Debussche , Julien Vovelle

We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…

Analysis of PDEs · Mathematics 2022-10-06 Ludovic Cesbron

We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the…

Analysis of PDEs · Mathematics 2019-04-03 Shrish Parmeshwar , Mahir Hadzic , Juhi Jang

In this article, we study the small dispersion limit of the Euler-Korteweg system in a domain with a smooth boundary and no-flux boundary conditions. We exploit a relative energy approach to study the convergence of finite energy weak…

Analysis of PDEs · Mathematics 2026-04-28 Paolo Antonelli , Yuri Cacchiò

We justify the global-in-time validity of Hilbert expansion for the ionic Vlasov-Poisson-Boltzmann system in $\mathbb{R}^3$, a fundamental model describing ion dynamics in dilute collisional plasmas. As the Knudsen number approaches zero,…

Analysis of PDEs · Mathematics 2026-01-06 Fucai Li , Yichun Wang

In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…

Analysis of PDEs · Mathematics 2020-05-14 Marcelo M. Disconzi , Chenyun Luo

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…

Analysis of PDEs · Mathematics 2026-05-08 Chenyun Luo , Junyan Zhang

In this paper, we study the two-dimensional compressible magneto-micropolar boundary layer equations on the half-plane, which are derived from 2D compressible magneto-micropolar fluid equations with the non-slip boundary condition on…

Analysis of PDEs · Mathematics 2025-04-17 Yuming Qin , Junchen Liu

We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes equations, we prove…

Analysis of PDEs · Mathematics 2017-12-29 Ning Jiang , Yi-Long Luo , Shaojun Tang

In this paper we establish a new convex integration approach for the barotropic compressible Euler equations in two space dimensions. In contrast to existing literature, our new method generates not only the momentum for given density, but…

Analysis of PDEs · Mathematics 2024-10-29 Simon Markfelder

We prove the existence of local-in-time smooth solutions of the incompressible semi-geostrophic equations expressed in Eulerian co-ordinates in 3-dimensional smooth bounded simply-connected domains. Our solutions adhere to Cullen's…

Analysis of PDEs · Mathematics 2018-07-26 Mark Wilkinson

We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…

Analysis of PDEs · Mathematics 2023-11-16 Igor Kukavica , Šárka Nečasová , Amjad Tuffaha

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

Analysis of PDEs · Mathematics 2020-01-03 Eduard Feireisl , Martina Hofmanová