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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 constructExpand
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Blowup of smooth solutions to the compressible Navier‐Stokes equation with compact density
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 immediateExpand
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Viscous limits for piecewise smooth solutions to systems of conservation laws
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 piecewiseExpand
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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 directlyExpand
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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 theExpand
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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
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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 initialExpand
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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 solutionsExpand
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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 onExpand
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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 ofExpand
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