Conditional Stable Soliton Resolution for a Semi-linear Skyrme Equation
Conditional Stable Soliton Resolution for a Semi-linear Skyrme Equation
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DOI：
10.1007/s40818-019-0072-5
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发表时间：
2017-03
期刊：
影响因子：
2.8
通讯作者：
A. Lawrie;Casey Rodriguez
中科院分区：
文献类型：
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作者：
A. Lawrie;Casey Rodriguez
我们研究了半线性版本的Skyrme系统由于阿德金斯和Nappi。在这个系统中的对象是从三维闵可夫斯基空间到3-球面和1-形式的映射，通过拉格朗日作用耦合。在一个共旋转对称约化下，我们建立了一族定态解的存在性、唯一性和无条件渐近稳定性，这些定态解的指数为映射的拓扑度.我们还证明了，一个任意大的等变扰动导致一个全球定义的解决方案，分散到在无限的时间，只要解决方案的临界范数仍然有界的最大区间上的存在的局部柯西理论。我们注意到，演化方程是超临界相对于保守的能量。
We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from-dimensional Minkowski space into the 3-sphere and 1-forms on, coupled via a Lagrangian action. Under a co-rotational symmetry reduction we establish the existence, uniqueness, and unconditional asymptotic stability of a family of stationary solutions, indexed by the topological degreeof the underlying map. We also prove that an arbitrarily large equivariant perturbation ofleads to a globally defined solution that scatters toin infinite time as long as the critical norm for the solution remains bounded on the maximal interval of existence given by the local Cauchy theory. We remark that the evolution equations are super-critical with respect to the conserved energy.