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Hành Vi Lớn Thời Gian của Hệ Thống Navier–Stokes–Fourier Nén Trong Toàn Bộ Không Gian
Tóm tắt
Bài báo hiện tại dành cho việc điều tra hành vi lâu dài về hệ thống Navier–Stokes–Fourier nén trong toàn bộ không gian. Dưới điều kiện rằng $$\Vert \rho \Vert _{C^\alpha }$$ và $$\Vert \rho , T\Vert _{L^\infty }$$ có ràng buộc đồng nhất theo thời gian, chúng tôi chứng minh rằng các nghiệm đều hội tụ về trạng thái cân bằng với tốc độ suy giảm tối ưu.
Từ khóa
#Hệ thống Navier–Stokes–Fourier #hành vi lớn thời gian #nghiệm đều #trạng thái cân bằng #nén.Tài liệu tham khảo
Bahouri, H., Chemin, J.-Y., Danchin, R.: Fourier Analysis and Nonlinear Partial Differential Equations. Fundamental Principles of Mathematical Sciences, vol. 343. Springer, Heidelberg (2011)
Charve, F., Danchin, R.: A global existence result for the compressible Navier–Stokes equations in the critical \(L^p\) framework. Arch. Ration. Mech. Anal. 198, 233–271 (2010)
Chen, Q., Miao, C., Zhang, Z.: Global well-posedness for compressible Navier–Stokes equations with highly oscillating initial velocity. Commun. Pure Appl. Math. 63(9), 1173–1224 (2010)
Chen, Q., Miao, C., Zhang, Z.: Well-posedness in critical spaces for the compressible Navier–Stokes equations with density dependent viscosities. Rev. Mat. Iberoam. 26(3), 915–946 (2010)
Chen, Q., Miao, C., Zhang, Z.: On the ill-posedness of the compressible Navier–Stokes equation in the critical Besov spaces. Rev. Mat. Iberoam. 31(4), 1375–1402 (2015)
Danchin, R.: Global existence in critical spaces for compressible Navier–Stokes equations. Invent. Math. 141, 579–614 (2000)
Danchin, R.: Local theory in critical spaces for compressible viscous and heat-conductive gases. Commun. Partial Differ. Equ. 26, 1183–1233 (2001)
Danchin, R.: Global existence in critical spaces for flows of compressible viscous and heat-conductive gases. Arch. Ration. Mech. Anal. 160, 1–39 (2001)
Danchin, R.: On the uniqueness in critical spaces for compressible Navier–Stokes equations. Nonlinear Differ. Equ. Appl. 12, 111–128 (2005)
Danchin, R., Xu, J.: Optimal decay estimates in the critical \(L^p\) framework for flows of compressible viscous and heat-conductive gases. Arch. Ration. Mech. Anal. 224, 53–90 (2017)
Fang, D., Zhang, T., Zi, R.: Decay estimates for isentropic compressible Navier–Stokes equations in bounded domain. J. Math. Anal. Appl. 386(2), 939–947 (2012)
He, L., Huang, J., Wang, C.: Global stability of large solutions to the 3D compressible Navier–Stokes equations. Arch. Ration. Mech. Anal. 234, 1167–1222 (2019)
Hoff, D.: Global solutions of the Navier–Stokes equations for multidimensional compressible flow with discontinuous initial data. J. Differ. Equ. 120, 215–254 (1995)
Hoff, D.: Discontinuous solutions of the Navier–Stokes equations for multidimensional flows of heat-conducting fluids. Arch. Rational Mech. Anal. 139, 303–354 (1997)
Huang, X., Li, J.: Global classical and weak solutions to the three-dimensional full compressible Navier–Stokes system with vacuum and large oscillations. Arch. Ration. Mech. Anal. 227, 995–1059 (2018)
Kagei, Y., Kobayashi, T.: On large time behavior of solutions to the compressible Navier–Stokes equations in the half space in \({{\mathbb{R}}}^3\). Arch. Ration. Mech. Anal. 165, 89–159 (2002)
Kagei, Y., Kobayashi, T.: Asymptotic behavior of solutions of the compressible Navier–Stokes equations on the half space. Arch. Ration. Mech. Anal. 177, 231–330 (2005)
Kobayashi, T.: Some estimates of solutions for the equations of motion of compressible viscous fluid in an exterior domain in \({{\mathbb{R}}}^3\). J. Differ. Equ. 184, 587–619 (2002)
Kobayashi, T., Shibata, Y.: Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain of \({{\mathbb{R}}}^3\). Commun. Math. Phys. 200, 621–659 (1999)
Matsumura, A., Nishida, T.: The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids. Proc. Jpn. Acad. Ser. A Math. Sci. 55, 337–342 (1979)
Matsumura, A., Nishida, T.: The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. 20, 67–104 (1980)
Serre, D.: Sur l‘équation monodimensionnelle d‘un fluide visqueux, compressible et conducteur de chaleur. C.R. Acad. Sc. Paris 303, 703–706 (1986)
Serre, D.: Variations de grande amplitude pour la densité d’un fluide visqueux compressible. Physics D 48, 113–128 (1991)
Sun, Y., Wang, C., Zhang, Z.: A Beale–Kato–Majda blow-up criterion for the 3-D compressible Navier–Stokes equations. J. Math. Pure Appl. 95, 36–47 (2011)
Sun, Y., Wang, C., Zhang, Z.: A Beale–Kato–Majda criterion for three dimensional compressible viscous heat-conductive flows. Arch. Ration. Mech. Anal. 201, 727–742 (2011)
Villani, C.: Hypocoercivity. Mem. Am. Math. Soc. 202(950) (2009)
Wen, H., Zhu, C.: Blow-up criterions of strong solutions to 3D compressible Navier–Stokes equations with vacuum. Adv. Math. 248, 534–572 (2013)
Zhang, Z., Zi, R.: Convergence to equilibrium for the solution of the full compressible Navier–Stokes equations. Ann. Inst. H. Poincaré Anal. Non Lineairé 37, 457–488 (2020)