|
|
Pure Mathematics 2026
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
|
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 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 ,其中
| [1] | Kato, T. (1984) Strong-Solutions for the Navier-Stokes Equation in, with Applications to Weak Solutions. Mathematische Zeitschrift, 187, 471-480。 |
| [2] | Cannone, M. (1995) Paraproduits et Navier-Stokes Diderot Editeur. Arts et Sciences. |
| [3] | Giga, Y. and Miyakawa, T. (1989) Navier-Stokes Flow in with Measures as Initial Vorticity and Morrey Space. Communications in Partial Differential Equations, 14, 577-618. https://doi.org/10.1080/03605308908820621 |
| [4] | Kato, T. (1992) Strong Solutions of the Navier-Stokes Equation in Morrey Spaces. Bulletin/Brazilian Mathematical Society, 22, 127-155. |
| [5] | Taylor, M.E. (1992) Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations. Communications in Partial Differential Equations, 17, 1407-1456. https://doi.org/10.1080/03605309208820892 |
| [6] | Coiculescu, M.P. and Palasek, S. (2025) Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data. Inventiones mathematicae. https://doi.org/10.1007/s00222-025-01396-z |
| [7] | Chamorro, D. and Mansais, M. (2025) Some General External Forces and Critical Mild Solutions for the Fractional Navier-Stokes Equations. Journal of Elliptic and Parabolic Equations, 11, 1071-1100. https://doi.org/10.1007/s41808-025-00365-0 |
| [8] | Lemarié-Rieusset, P.G. (2018) Sobolev Multipliers, Maximal Functions and Parabolic Equations with a Quadratic Nonlinearity. Journal of Functional Analysis, 274, 659-694. https://doi.org/10.1016/j.jfa.2017.11.009. |
| [9] | Lemarié-Rieusset, P.G. (2016) The Navier-Stokes Problem in the 21st Century. CRC Press. |
| [10] | Wu, G. and Yuan, J. (2008) Well-Posedness of the Cauchy Problem for the Fractional Power Dissipative Equation in Critical Besov Spaces. Journal of Mathematical Analysis and Applications, 340, 1326-1335. https://doi.org/10.1016/j.jmaa.2007.09.060 |