广义旋转Navier-Stokes方程解的整体适定性和解析性

王伟华

数学学报 ›› 2020, Vol. 63 ›› Issue (5) : 417-426.

PDF(570 KB)
PDF(570 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (5) : 417-426. DOI: 10.12386/A2020sxxb0036
论文

广义旋转Navier-Stokes方程解的整体适定性和解析性

    王伟华
作者信息 +

Global Well-posedness and Analyticity for the Generalized Rotating Navier-Stokes Equations

    Wei Hua WANG
Author information +
文章历史 +

摘要

αq满足适当的条件下,当初值属于Fourier-Herz空间?q1-2α(R3)时,我们建立了广义3维不可压旋转Navier-Stokes方程温和解的整体适定性和解析性.作为推论,我们也给出了广义Navier-Stokes方程的相应结论.

Abstract

We establish the global well-posedness and analyticity of mild solution to the generalized three-dimensional incompressible Navier–Stokes equations for rotating fluids if the initial data are in Fourier–Herz spaces ?q1-2α (R3) under appropriate conditions for α and q. As corollaries, we also give the corresponding conclusions of the generalized Navier–Stokes equation.

关键词

不可压 / 旋转流体 / Fourier-Herz空间 / 分数阶Navier-Stokes方程

Key words

incompressible / rotating fluids / Fourier-Herz spaces / fractional Navier-Stokes equations

引用本文

导出引用
王伟华. 广义旋转Navier-Stokes方程解的整体适定性和解析性. 数学学报, 2020, 63(5): 417-426 https://doi.org/10.12386/A2020sxxb0036
Wei Hua WANG. Global Well-posedness and Analyticity for the Generalized Rotating Navier-Stokes Equations. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 417-426 https://doi.org/10.12386/A2020sxxb0036

参考文献

[1] Babin A., Mahalov A., Nicolaenko B., Regularity and integrability of 3D Euler and Navier-Stokes equations for rotating fluids, Asymptot. Anal., 1997, 15(2):103-150.
[2] Babin A., Mahalov A., Nicolaenko B., Global regularity of 3D rotating Navier-Stokes equations for resonant domains, Indiana Univ. Math. J., 1999, 48(3):1133-1176.
[3] Babin A., Mahalov A., Nicolaenko B., 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity, Indiana Univ. Math. J., 2001, 50(Suppl):1-35.
[4] Bae H., Existence and analyticity of Lei-Lin solution to the Navier-Stokes equations, Proc. Amer. Math. Soc., 2015, 143(3):2887-2892.
[5] Bae H., Biswas A., Tadmor E., Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces, Arch. Ration. Mech. Anal., 2012, 205(9):963-991.
[6] Bahouri H., Chemin J. Y., Danchin R., Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), Vol. 343, Springer, Heidelberg, 2011.
[7] Cannone M., Wu G., Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces, Nonlinear Anal., 2012, 75(9):3754-3760.
[8] Chemin J. Y., Gallagher I., Large, global solutions to the Navier-Stokes equations, slowly varying in one direction, Trans. Amer. Math. Soc., 2010, 362(6):2859-2873.
[9] Chemin J. Y., Desjardins B., Gallagher I., et al., Mathematical Geophysics, An Introduction to Rotating Fluids and the Navier-Stokes Equations, Oxford Lecture Series in Mathematics and its Applications 32, Oxford University Press, Oxford, 2006.
[10] Dragi?evi? O., Petermichl S., Volberg A., A rotation method which gives linear Lp estimates for powers of the Ahlfors-Beurling operator, J. Math. Pures Appl., 2006, 86(6):492-509.
[11] Fang D., Han B., Hieber M., Global existence results for the Navier-Stokes equations in the rotational framework in Fourier-Besov spaces, in W. Arendt, R. Chill, Y. Tomilov (eds.), Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Birkhauser, Cham, 2015.
[12] Fang D., Han B., Hieber M., Local and global existence results for the Navier-Stokes equations in the rotational framework, Commun. Pure Appl. Anal., 2015, 14(2):609-622.
[13] Foias C., Temam R., Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 1989, 87(2):359-369.
[14] Giga Y., Inui K., Mahalov, A., Matsui S., Navier-Stokes equations in a rotating frame in R3 with initial data nondecreasing at infinity, Hokkaido Math. J., 2006, 35(2):321-364.
[15] Hieber M., Shibata Y., The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework, Math. Z., 2010, 265(2):481-491.
[16] Iwabuchi T., Global well-posedness for Keller-Segel system in Besov type spaces, J. Math. Anal. Appl., 2011, 379(2):930-948
[17] Iwabuchi T., Takada R., Global solutions for the Navier-Stokes equations in the rotational framework, Math. Ann., 2013, 357(2):727-741.
[18] Iwabuchi T., Takada R., Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type, J. Funct. Anal., 2014, 267(5):1321-1337.
[19] Konieczny P., Yoneda T., On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations, J. Differential Equations, 2011, 250(10):3859-3873.
[20] Ladyzhenskaya O. A., Unique global solvability of the three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry (in Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Math. Inst. Steklov. (LOMI), 1968, 7:155-177.
[21] Lei Z., Lin F., Global mild solutions of Navier-Stokes equations, Comm. Pure Appl. Math., 2011, 64(2):1297-1304.
[22] Lemarié-Rieusset P. G., Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC Research Notes in Mathematics, Vol. 431, Chapman & Hall/CRC, Boca Raton, FL, 2002.
[23] Lions J. L., Quelques Méthodes de Résolution des Problémes aux Limites Nonlinéaires, Donud, Paris, 1969.
[24] Liu Q., Zhao J., Global well-posedness for the generalized magneto-hydrodynamic equations in the critical Fourier-Herz spaces, J. Math. Anal. Appl., 2014, 420(2):1301-1315.
[25] Sun J., Yang M., Cui S., Existence and analyticity of mild solutions for the 3D rotating Navier-Stokes equations, Ann. Mat. Pura Appl., 2017, 196(4):1203-1229.
[26] Triebel H., Theory of Function Spaces. Monographs in Mathematics, Birkhäuser Verlag, Basel, 1983.
[27] Wang W., Global existence and analyticity of mild solutions for the stochastic Navier-Stokes-Coriolis equations in Besov spaces, Nonlinear Anal. Real World Appl., 2020, 52:103048pp.
[28] Wang W., Wu G., Global mild solution of the generalized Navier-Stokes equations with the Coriolis force, Appl. Math. Lett., 2018, 76(2):181-186.
[29] Wu J., The generalized incompressible Navier-Stokes equations in Besov spaces, Dyn. Partial Diff. Equ., 2004, 1(4):381-400.
[30] Wu J., Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces, Comm. Math. Phys., 2006, 263(3):803-831.
[31] Zhang P., Zhang T., Global axisymmetric solutions to three-dimensional Navier-Stokes system, Int. Math. Res. Not. IMRN, 2014, 2014(3):610-642.

基金

国家自然科学基金(11771423,11871452);中国国家自然科学基金委员会与韩国国家研究基金会联合资助合作交流项目(1191101060);江苏省高等学校自然科学研究面上项目(19KJD100007)

PDF(570 KB)

Accesses

Citation

Detail

段落导航
相关文章

/