Lin Zheng
Beijing University of Technology, China
Title: Finite-time blow-up for the 3-D primitive equations of oceanic and atmospheric dynamics
Biography
Biography: Lin Zheng
Abstract
In this paper, we prove that for certain class of initial data, the corresponding solutions of the 3-D primitive equations of oceanic and atmospheric without viscosity and with periodic boundary conditions blow up in finite time. We reduce the unknown function of the three dimensional by constructing special solution and consider the restriction of the evolution of equation on the surface x=0, y=0. Furthermore, we construct a self-similar solution to solve the blow-up problem.
Recent Publications
1. C J Liu, Y G Wang and T Yang (2014) A well-posedness theory for the Prandtl equations in three space variables. Adv. Math. 308:1074--1126.
2. C. Cao,Slim,J. K. Li, E. S. Titi (2012) Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Comm. Math. Phys. 337:473--482.
3. C. Cao,J. k. Li, E. S. Titi (2014)Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivty. JDE 257:4108--4132.
4. C. Cao, E. S. Titi (2012) Global well-posedness of the three-dimensional straified primitive equations with partial vertical mixing turbulence diffusion. Comm. Math.Phys. 310: 537--568.
5. B. Guo, D. Huang (2011) Existence of the universal attractor for the 3D viscous primitive equations of large-scale moist atmosphere. JDE. 47: 457--491.