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Publications Influence

The relaxation schemes for systems of conservation laws in arbitrary space dimensions

We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct… Expand

848 125

Blowup of smooth solutions to the compressible Navier‐Stokes equation with compact density

- Z. Xin
- Mathematics
- 1 March 1998

We present a sufficient condition on the blowup of smooth solutions to the compressible Navier-Stokes equations in arbitrary space dimensions with initial density of compact support. As an immediate… Expand

357 29

Viscous limits for piecewise smooth solutions to systems of conservation laws

- J. Goodman, Z. Xin
- Mathematics
- 1 September 1992

In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise… Expand

171 29

On the weak solutions to a shallow water equation

We obtain the existence of global-in-time weak solutions to the Cauchy problem for a one-dimensional shallow-water equation that is formally integrable and can be obtained by approximating directly… Expand

431 25

On the regularity of weak solutions to the magnetohydrodynamic equations

Abstract In this paper, we study the regularity of weak solution to the incompressible magnetohydrodynamic equations. We obtain some sufficient conditions for regularity of weak solutions to the… Expand

325 20- PDF

On the global existence of solutions to the Prandtl's system

Abstract In this paper we establish a global existence of weak solutions to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik (J. Appl. Math. Mech.… Expand

149 17- PDF

Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in three spatial dimensions with smooth initial… Expand

255 16- PDF

Vacuum states for compressible flow

In this paper we study the evolutions of the interfaces between
gases and the vacuum for both inviscid and viscous one dimensional
isentropic gas motions. The local (in time) existence of solutions… Expand

209 13

Frequent duplication and deletion events in the 5S RNA genes and the associated spacer regions of theTriticeae

The 5 S DNA units from 15 grasses in theTriticeae were analysed at the DNA sequence level. Four units carried duplications near the 3′-end of the 5 S RNA gene with 3 of the duplications centred on… Expand

124 11

On the vanishing viscosity limit for the 3D navier-stokes equations with a slip boundary condition

where and below ∇· and ∇× denote the div and curl operators respectively, n is the outward normal, and τ is the unit tangential vector of ∂Ω. The investigation of vanishing viscosity limit of… Expand

175 11- PDF