On initial-boundary value problem of the stochastic Navier–Stokes equations in the half space

References

• Bensoussan, A., Temam, R. ( 1973). Equations stochastiques du type Navier-Stokes. J. Funct. Anal. 13(2):195–222. doi:10.1016/0022-1236(73)90045-1.
   Google Scholar
• Foiaş, C. ( 1973). Statistical study of Navier-Stokes equations II. Rend. Sem. Mat. Univ. Padova. 49:9–123.
   Google Scholar
• Capinski, M., Gatarek, D. ( 1994). Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension. J. Funct. Anal. 126(1):26–35. doi:10.1006/jfan.1994.1140.
   Web of Science ®Google Scholar
• Mikulevicius, R., Rozovskii, B. L. ( 2005). Global L2-solutions of stochastic Navier-Stokes equations. Ann. Probab. 33:137–176.
   Google Scholar
• Kim, J. U. ( 2010). Strong solutions of the stochastic Navier-Stokes equations in R3. Indiana Univ. Math. J. 59(4):1417–1450. doi:10.1512/iumj.2010.59.3930.
   Web of Science ®Google Scholar
• Taniguchi, T. ( 2011). The existence of energy solutions to 2-dimensional non-Lipschitz stochastic Navier–Stokes equations in unbounded domains. J. Differ. Equ. 251(12):3329–3362. doi:10.1016/j.jde.2011.07.029.
   Web of Science ®Google Scholar
• Flandoli, F., Gatarek, D. ( 1995). Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Relat. Fields. 102(3):367–391. doi:10.1007/BF01192467.
   Web of Science ®Google Scholar
• Flandoli, F., Romito, M. ( 2008). Markov selections for the 3D stochastic Navier–Stokes equations. Probab. Theory Relat. Fields. 140(3-4):407–458. doi:10.1007/s00440-007-0069-y.
   Web of Science ®Google Scholar
• Flandoli, F., ( 2008). An introduction to 3D stochastic fluid dynamics. In SPDE in Hydrodynamic: Recent Progress and Prospects, Vol. 1942. Berlin: Springer, pp. 51–150.
   Google Scholar
• Kuksin, S., Shirikyan, A. ( 2012). Mathematics of two-dimensional turbulence. In Cambridge Tracts in Mathematics, Vol. 194. Cambridge: Cambridge University Press.
   Google Scholar
• Breit, D., Feireisl, E., Hofmanová, M. ( 2018). Stochastically forced compressible fluid flows. In De Gruyter Series in Applied and Numerical Mathematics, Vol. 3. Berlin: De Gruyter.
   Google Scholar
• Fujita, H., Kato, T. ( 1964). On the Navier-Stokes initial value problem. I. Arch. Rational Mech. Anal. 16(4):269–315. doi:10.1007/BF00276188.
   Web of Science ®Google Scholar
• Cannone, M. ( 1995). Ondelettes, paraproduits et Navier-Stokes (French). Paris: Diderot Editeur. pp x+191.
   Google Scholar
• Koch, H., Tataru, D. ( 2001). Well-posedness for the Navier–Stokes Equations. Adv. Math. 157(1):22–35. doi:10.1006/aima.2000.1937.
   Web of Science ®Google Scholar
• Bahouri, H., Chemin, J.-Y., Danchin, R. ( 2011). Fourier analysis and nonlinear partial differential equations. In Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, Vol. 343, Heidelberg: Springer.
   Google Scholar
• Du, L., Zhang, T. ( 2020). Local and global strong solutions to the stochastic incompressible Navier-Stokes equations in critical Besov space. J. Math. Anal. Appl. 481(1):16.
   Web of Science ®Google Scholar
• Krylov, N. V. ( 1999). An analytic approach to SPDEs. In Stochastic Partial Differential Equations: Six Perspectives, Vol. 64. Providence, RI: Amer. Math. Soc., pp. 185–242.
   Google Scholar
• Crispo, F., Maremonti, P. ( 2004). On the (x, t) asymptotic properties of solutions of the Navier-Stokes equations in the half-space. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI). 318:147–202. Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts.
   Google Scholar
• Solonnikov, V. A. ( 2003). On nonstationary Stokes problem and Navier-Stokes problem in a half-space with initial data nondecreasing at infinity. J. Math. Sci. (N. Y.). 114(5):1726–1740.
   Google Scholar
• Dou, J., Ma, J. ( 2023). Hardy-Littlewood-Sobolev inequalities with partial variable weght on the upper half space and related inequalities. arXiv:2308.06976.
   Google Scholar
• Solonnikov, V. A. ( 1976). Estimates of the solution of a certain initial-boundary value problem for a linear nonstationary system of Navier-Stokes equations. In Boundary Value Problems of Mathematical Physics and Related Questions in the Theory of Functions, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI). Russian Mathematical Surveys. Vol. 59, 178–257.
   Google Scholar
• Chang, T., Kang, K. ( 2018). Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space. Ann. Univ. Ferrara. 64(1):47–82. doi:10.1007/s11565-017-0287-x.
   Google Scholar
• Chang, T., Jin, B. J. ( 2016). Initial and boundary values for Lαq (Lp) solution of the Navier–Stokes equations in the half-space. J. Math. Anal. Appl. 439(1):70–90. doi:10.1016/j.jmaa.2016.02.052.
   Web of Science ®Google Scholar
• Chang, T., Jin, B. J. ( 2020). Global well-posedness of the half-space problem of the Navier-Stokes equations in critical function spaces of limiting case. Ann. Univ. Ferrara Sez. VII Sci. Mat. 66:273–294.
   Google Scholar
• Chang, T., Jin, B. J. ( 2019). Global in time solvability of the Navier-Stokes equations in the half-space. J. Differ. Equ. 267(7):4293–4319. doi:10.1016/j.jde.2019.04.037.
   Web of Science ®Google Scholar
• Bergh, J., Löfström, J. ( 1976). Interpolation spaces. An introduction. In Grundlehren der Mathematischen Wissenschaften. Berlin-New York: Springer-Verlag.
   Google Scholar