16 citations · 51 across the 19 of their papers we have counts for
20 papers
Global solutions to the Boussinesq equations and the planetary geostrophic approximation
Ryan Budahazy, Xin Liu
We investigate the three dimensional Boussinesq equations in the planetary geostrophic scale, where the buoyancy/gravity driven flow is near geostrophic balance in the large horizo…
The traveling wave solutions of the 1D hyperbolic Keller-Segel equations
Xin Liu, William Kyle Barker
The goal of this paper is to investigate the traveling wave solutions with one-sided far field conditions for the one-dimensional hyperbolic Keller-Segel equations with quorum sens…
Rigorous justification of the hydrostatic-incompressible approximation for weakly stratified isothermal flow
Quyuan Lin, Xin Liu
We consider the limit of small Mach number and small vertical-to-horizontal aspect ratio for the isothermal compressible Navier-Stokes system. In addition, we consider the scale in…
Zero Mach Number Limit of the Compressible Primitive Equations: Ill-prepared Initial Data
Xin Liu, Edriss S. Titi
In the work, we consider the zero Mach number limit of compressible primitive equations in the domain or . We ide…
Immediate blowup of entropy-bounded classical solutions to the vacuum free boundary problem of non-isentropic compressible Navier--Stokes equations
Xin Liu, Yuan Yuan
This paper considers the immediate blowup of entropy-bounded classical solutions to the vacuum free boundary problem of non-isentropic compressible Navier-Stokes equations. The vis…
On the resolvability of the dynamics of one fluid flow via a testing fluid in a two-fluids flow model
Xin Liu
In this work, by considering an isentropic fluid-fluid interaction model with a large symmetric drag force, a commonly used simplified two-fluids flow model is justified as the asy…
On the effect of fast rotation and vertical viscosity on the lifespan of the primitive equations
Quyuan Lin, Xin Liu, Edriss S. Titi
We study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stok…
Well-posedness of Hibler's dynamical sea-ice model
Xin Liu, Marita Thomas, Edriss S. Titi
This paper establishes the local-in-time well-posedness of solutions to an approximating system constructed by mildly regularizing the dynamical sea-ice model of {\it W.D. Hibler,…
Poisson stable solutions for stochastic differential equations with Lévy noise
Xin Liu, Zhenxin Liu
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost r…
Well-posedness of strong solutions to the anelastic equations of stratified viscous flows
Xin Liu, Edriss S. Titi
We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interacti…
Zero Mach Number Limit of the Compressible Primitive Equations Part I: Well-prepared Initial Data
Xin Liu, Edriss S. Titi
This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting e…
Well-posedness of the viscous equations with strong stratification
Xin Liu
This is the old version of this project. Please find the new version at 1906.12233.
On the self-similar solution to full compressible Navier-Stokes equations without heat conductivity
Xin Liu, Yuan Yuan
In this work, we establish a class of globally defined, large solutions to the free boundary problem of compressible Navier-Stokes equations with constant shear viscosity and vanis…
Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities
Xin Liu, Edriss S. Titi
We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the ca…
Local Well-posedness of Strong Solutions to the Three-dimensional Compressible Primitive Equations
Xin Liu, Edriss S. Titi
This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is s…
Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D
Xin Liu, Yuan Yuan
In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dim…
On the Expanding Configurations of Viscous Radiation Gaseous Stars: Isentropic and Thermodynamic Models
Xin Liu
In this work, we study the stability of the expanding configurations for radiation gaseous stars. Such expanding configurations exist for the isentropic model and the thermodynamic…
Compressible Viscous Flows in a Symmetric Domain with Complete Slip Boundary
Xin Liu
This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides fri…
Global Solutions to Compressible Navier-Stokes Equations With Spherically Symmetric Motion and Free Boundary
Xin Liu
This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for…
A Model of Radiational Gaseous Stars
Xin Liu
We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describin…