English
Related papers

Related papers: Global Well-posedness for the Primitive Equations …

200 papers

This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local…

Numerical Analysis · Mathematics 2024-07-09 Soonpil Kang , James F. Kelly , Anthony P. Austin , Francis X. Giraldo

We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is described by a step function, with a jump discontinuity across…

Analysis of PDEs · Mathematics 2016-11-21 Rafael Granero-Belinchón , Steve Shkoller

This paper is concerned with the global well-posedness of the two-dimensional incompressible vorticity equation in the half plane. Under the assumption that the initial vorticity $\omega_0\in W^{k,p}(\R^{2}_+)$ with $k\geq3$ and $1<p<2$, it…

Analysis of PDEs · Mathematics 2021-11-03 Quansen Jiu , You Li , Wanwan Zhang

Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…

Analysis of PDEs · Mathematics 2025-07-10 Jiahong Wu , Fuyi Xu , Xiaoping Zhai

The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…

Analysis of PDEs · Mathematics 2024-12-24 Dieter Bothe , Mathis Fricke , Kohei Soga

We establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system. The primary application of this abstract framework is to infer the local existence of…

Analysis of PDEs · Mathematics 2015-05-19 Arnaud Debussche , Nathan Glatt-Holtz , Roger Temam

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…

Fluid Dynamics · Physics 2010-11-03 Helmut Abels , Harald Garcke , Günther Grün

The statistically steady humidity distribution resulting from an interaction of advection, modeled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modeled as immediate condensation whenever the…

Fluid Dynamics · Physics 2011-05-04 Jai Sukhatme , William R. Young

Shallow Water Moment Equations are reduced-order models for free-surface flows that employ a vertical velocity expansion and derive additional so-called moment equations for the expansion coefficients. Among desirable analytical properties…

Numerical Analysis · Mathematics 2026-04-08 Julian Koellermeier

One significant difference between the atmospheres of stars and exoplanets is the presence of condensed particles (clouds or hazes) in the atmosphere of the latter. The main goal of this paper is to develop a self-consistent microphysical…

Earth and Planetary Astrophysics · Physics 2015-06-11 A. Zsom , L. Kaltenegger , C. Goldblatt

Cloud microphysical parameterizations in atmospheric models describe the formation and evolution of clouds and precipitation, a central weather and climate process. Cloud-associated latent heating is a primary driver of large and…

We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density…

Analysis of PDEs · Mathematics 2007-07-07 Debora Amadori , Andrea Corli

This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…

Analysis of PDEs · Mathematics 2017-11-17 Zhong Tan , Yanjin Wang

Multiphase poromechanics describes the evolution of multiphase flow in deformable porous media. Mathematical models for such multiphysics system are inheritely nonlinear, potentially degenerate and fully coupled systems of partial…

Analysis of PDEs · Mathematics 2023-12-05 Jakub Wiktor Both , Clément Cancès

The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…

Analysis of PDEs · Mathematics 2022-07-04 Jing Li , Boqiang Lü , Xue Wang

By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however of the Young Laplace equation becomes tricky when a…

Soft Condensed Matter · Physics 2013-06-05 Nikolaos T. Chamakos , Michail E. Kavousanakis , Athanasios G. Papathanasiou

The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature,…

Analysis of PDEs · Mathematics 2022-11-02 Yunkun Chen , Yi Peng , Xue Wang

We study the structural and thermodynamic properties of a model of point particles interacting by means of a Gaussian pair potential first introduced by Stillinger [Stillinger F H 1976 J. Chem. Phys. 65, 3968]. By employing integral…

Soft Condensed Matter · Physics 2009-10-31 A. Lang , C. N. Likos , M. Watzlawek , H. Lowen

We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence…

Analysis of PDEs · Mathematics 2022-03-15 Yang Liu , Xin Zhong

We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…

Analysis of PDEs · Mathematics 2024-04-04 Raphaël Danchin