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一类带外力项的半线性抛物方程在抛物型Morrey空间中的整体适定性
Global Well-Posedness of a Class of Semilinear Parabolic Equations with External Force in Parabolic Morrey Spaces

DOI: 10.12677/pm.2026.161022, PP. 192-203

Keywords: Navier-Stokes方程,温和解,临界空间,抛物型Morrey空间,尺度不变性
Navier-Stokes Equations
, Mild Solution, Critical Space, Parabolic Morrey Space, Scale Invariance

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Abstract:

本文研究了一类带外力项的广义半线性抛物方程在抛物型Morrey空间 M α p 1 , k( d+α ) α?β 中的整体适定性问题。该方程包含分数阶拉普拉斯算子耗散项、非局部非线性项及一般外力项,其形式为 u t + ( ?Δ ) α 2 u= ( ?Δ ) β 2 ( | u | k u )+f ,其中 β<α<( k+1 )β

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