In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with "small" initial data. We first present some estimates on...In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with "small" initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with "small" initial data.展开更多
The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite...The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.展开更多
基金supported in part by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)the Henan Provincial Natural Science Foundation of China(152300410226)
文摘In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with "small" initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with "small" initial data.
基金Project supported by the National Natural Science Foundation of China(No. 10571024)the Natural Science Foundation of Henan Province of China (No.200510078005)the Science Foundation of Educational Department of Henan Province of China (No.200511051700)
文摘The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.