In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.
In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this proced...In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.展开更多
Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation ...Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.展开更多
基金This research is partially supported by the National Natural Science Foundation of China, and Science Foundation for the Excellent Young Teacher of Henan Province.
文摘In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.
文摘In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.
文摘Einstein＇s equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein＇s whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein＇s equation and the metric tensor.
