Related papers: On the Classical Solutions of Two Dimensional Invi…
In this paper, we establish the local-in-time well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow water in two dimensions. The solutions are shown to possess higher-order…
This paper establishes the global existence of smooth solutions to the 2D isentropic and irrotational Euler equations for Chaplygin gases with a general class of short pulse initial data, which, in particular, resolves in this special case,…
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…
For two dimensional inhomogeneous Navier-Stokes of incompressible flows, with the assumption that the viscosity depends on the density but with a positive lower bound, using a partial regularity approach, in particular some enhanced decay…
The paper examines one-dimensional total variation flow equation with Dirichlet boundary conditions. Thanks to a new concept of "almost classical" solutions we are able to determine evolution of facets -- flat regions of solutions. A key…
We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show…
In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two…
In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D…
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We…
We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric…
This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space $\mathbb{R}^2$, the partially…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partial\Omega.$ By some new estimates on the boundary related…
In this article we consider one-dimensional scalar quasilinear Klein--Gordon equations with general nonlinearities, on both $\mathbb{R}$ and $\mathbb{T}$. By employing a refined modified-energy framework of Ifrim and Tataru, we investigate…
We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…
In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and…
We prove the global existence and uniqueness of smooth solutions to the one-dimensional barotropic Navier-Stokes system with degenerate viscosity $\mu(\rho)=\rho^\alpha$. We establish that the smooth solutions have possibly two different…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on…