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Asymptotic behavior for the heat equation in nonhomogeneous media with critical density
heat equation non-homogeneous media singular density asymptotic behavior radially symmetric solutions
2012/6/21
We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). ...
A Lagrangian approach for the incompressible Navier-Stokes equations with variable density
Inhomogeneous Navier-Stokes equations critical regularity piecewise constant density Besov spaces Lagrangian coordinates
2011/9/6
Abstract: Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of...
Density of rational points on elliptic surfaces
Density of rational points elliptic surfaces
2010/12/9
Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V , not equal to V , such tha...
Vanishing Viscosity Limit for Isentropic Navier-Stokes Equations with Density-dependent Viscosity
compressible Navier-Stokes compressible Euler equations
2010/12/9
In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isen-tropic compressible Euler equatio...