论文标题
在时间和空间中具有分数衍生物的非本地传输扩散方程的某些存在和规律性结果
Some existence and regularity results for a non-local transport-diffusion equation with fractional derivatives in time and space
论文作者
论文摘要
我们研究了非线性传输扩散方程的全球弱解决方案的存在，并在时间变量中具有分数衍生物，在一些额外的假设下，我们还研究了这种类型的溶液的一些规律性。在此处考虑的系统中，扩散算子由分数拉普拉斯给出，假定非线性漂移是无分歧的，并且假定它可以满足Lebesgue空间中某些一般稳定性和界限。
We study the existence of global weak solutions of a nonlinear transport-diffusion equation with a fractional derivative in the time variable and under some extra hypotheses, we also study some regularity properties for this type of solutions. In the system considered here, the diffusion operator is given by a fractional Laplacian and the nonlinear drift is assumed to be divergence free and it is assumed to satisfy some general stability and boundedness properties in Lebesgue spaces.
