Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
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DOI：
10.1007/bf03167864
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发表时间：
1984-09
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影响因子：
--
通讯作者：
S. Ukai
中科院分区：
文献类型：
--
作者：
S. Ukai
讨论了无截断近似的无限域势的非线性Bolzmann方程。对于空间均匀和非均匀两种情况，柯西问题在时间上都是局部求解的。对于前一种情况，这是在速度变量中的Gevrey类的函数空间中进行的，对于后一种情况，是在空间变量中解析的函数的空间中进行的，对于速度变量中的Gevrey类的函数空间中是这样做的。所得到的存在定理是柯西-科瓦列夫斯基型的。同时，证明了Grad角截断近似的收敛性质。
The nonlinear Bolzmann equation is discussed without cutoff approximations on potentials of infinite range. The Cauchy problem is solved locally in time, for both the spatially homogeneous and inhomogeneous cases. For the former case, this is done in function spaces of Gevrey classes in the velocity variables, and for the latter, in spaces of functions which are analytic in the space variables and of Gevrey classes in the velocity variables. The obtained existence theorem is of Cauchy-Kowalewski type. Also, the convergence of Grad’s angular cutoff approximations is established.