arXiv subjects

C. -J Xu

Publications and source records attributed to C. -J Xu.

2 recordsLinked to original sources

arXiv2017

Analytical smoothing effect of solution for the boussinesq equations

In this paper, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H 1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equation admet exactly same smoothing effect properties of incompressible Navier-Stokes equations.

math.AP↗

arXiv2014

Local solvability of the $k$-Hessian equations

In this work, we study the existence of local solutions in $\mathbb{R}^{n}$ to $k$-Hessian equation,for which the nonhomogeneous term $f$ is permitted to change the sign or be non negative; if $f$ is $C^\infty,$ so is the local solution. We also give a classification for the second order polynomial solutions to the $k-$Hessian equation, it is the basis to construct the local solutions and obtain the uniform ellipticity of the linearized operators at such constructed local solutions.

math.AP↗