发表机构
School of Mathematics and Statistics, Wuhan University; Department of Mathematics Sciences, Graduate School of Science, Kyoto University; School of Mathematical Sciences, University of Science and Technology of China（武汉大学数学与统计学院; 京都大学理学研究科数学科学系; 中国科学技术大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对各向异性混合勒贝格空间中带粗糙无散漂移项的动力学福克-普朗克方程，结合能量抵消、各向异性正则化估计与De Giorgi迭代，建立弱次解局部有界性并证明超临界区域柯西问题整体适定性。
AI 中文摘要
我们在各向异性混合勒贝格空间中研究带粗糙无散漂移项的动力学福克-普朗克方程。无散结构产生的能量抵消在动力学局域化下仍有效，结合该抵消项、各向异性正则化估计及De Giorgi迭代，我们建立弱次解的局部有界性，进而得到标度超临界区域柯西问题的整体适定性。
英文摘要
We investigate kinetic Fokker--Planck equations with rough divergence-free drifts in anisotropic mixed Lebesgue spaces. The divergence-free structure yields an energy cancellation that remains effective under kinetic localization. Combining this cancellation with anisotropic regularization estimates and a De Giorgi iteration, we establish local boundedness for weak subsolutions and, consequently, global well-posedness for the Cauchy problem in a scaling-supercritical regime.
