arXiv subjects

Yan-Fang Peng

Publications and source records attributed to Yan-Fang Peng.

2 recordsLinked to original sources

arXiv2018

Exponential Decay for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations in 3D Bounded Domains

For barotropic compressible Navier-Stokes equations in three-dimensional (3D) bounded domains, we prove that any finite energy weak solution obtained by Lions [Mathematical topics in fluid mechanics, Vol. 2. Compressible models(1998)] and Feireisl-Novotný-Petzeltová [J. Math. Fluid Mech. 3(2001), 358-392] decays exponentially to the equilibrium state. This result is established by both using the extra integrability of the density due to Lions and constructing a suitable Lyapunov functional just under the framework of Lions-Feireisl's weak solutions.

math.AP↗

arXiv2017

Existence, non-degeneracy of proportional positive solutions and least energy solutions for a fractional elliptic system

In this paper, we study the following fractional nonlinear Schrödinger system $$ \left\{% \begin{array}{ll} (-Δ)^s u +u=μ_1 |u|^{2p-2}u+β|v|^p|u|^{p-2}u,~~x\in \R^N,\vspace{2mm}\\ (-Δ)^s v +v=μ_2 |v|^{2p-2}v+β|u|^p|v|^{p-2}v,~~x\in \R^N, \end{array}% \right. $$ where $0 0, μ_2>0, 1 2s$, and $β\in \R$ is a coupling constant. We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $μ_1,μ_2, p, β$. We also prove that the least energy vector solutions must be proportional and unique under some additional assumptions.

math.AP↗