论文标题
动力学最大$ l^p $ - 具有时间重量的及时性和对准动力学扩散方程的应用
Kinetic maximal $L^p$-regularity with temporal weights and application to quasilinear kinetic diffusion equations
论文作者
论文摘要
我们介绍了具有时间权重的动力学最大$ l^p $的概念，并证明了（分数）kolmogorov方程满足了此属性。我们表明，解决方案与痕量空间中的值是连续的，尤其是证明可以通过各向异性BESOV空间来表征痕量空间。我们进一步扩展了具有可变系数的Kolmogorov方程的动力学最大$ l^p_μ$的属性。最后，我们展示了如何使用动力学最大$ l^p_μ$ - 限制性来获得一类准线性动力学方程的局部溶液，并通过准线性动力学扩散方程来说明我们的结果。
We introduce the concept of kinetic maximal $L^p$-regularity with temporal weights and prove that this property is satisfied for the (fractional) Kolmogorov equation. We show that solutions are continuous with values in the trace space and prove, in particular, that the trace space can be characterized in terms of anisotropic Besov spaces. We further extend the property of kinetic maximal $L^p_μ$-regularity to the Kolmogorov equation with variable coefficients. Finally, we show how kinetic maximal $L^p_μ$-regularity can be used to obtain local existence of solutions to a class of quasilinear kinetic equations and illustrate our result with a quasilinear kinetic diffusion equation.
