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An N-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems
Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise
1. | College of Science, National University of Defense Technology, Changsha, 410073, China |
2. | School of Mathematics, South China University of Technology, Guangzhou, 510640, China |
We present the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Ulenbeck equations, and establish the existence and uniqueness of mild solutions for time fractional and space nonlocal stochastic Boussinesq equations driven by Gaussian white noise.
References:
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J. Huang, T. Shen and Y. Li,
Dynamics of stochastic fractional Boussinesq equations, Discre. Continu. Dynam. Syst.-B, 20 (2015), 2051-2067.
doi: 10.3934/dcdsb.2015.20.2051. |
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J. Lions,
Sur l'existence de solution des équation de Navier-Stokes, C. R. Acad. Sci. Pairs, 248 (1959), 2847-2849.
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F. Mainardi,
Fractional Calculus and Waves in Linear Viscoelasticity, Imperrial College Press, London, 2010. |
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M. Shinbrot,
Fractional derivatives of solutions of the Navier-stokes equations, Arch. Ration. Mech. Anal., 40 (1971), 139-154.
|
[10] |
Y. Wang, J. Xu and P. Kloeden,
Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative, Nonlin. Anal., 135 (2016), 205-222.
doi: 10.1016/j.na.2016.01.020. |
[11] |
C. Zeng and Q. Yang, Mild solution of time fractional Navier-Stokes equations driven by fractional Brownian motion, Preprint, 2017.
doi: 10.1016/j.spa.2017.03.013. |
[12] |
Y. Zhou and L. Peng,
Weak solutions of the time-fractional Navier-Stokes equations and optimal control, Compu. Math. Appl., 73 (2017), 1016-1027.
doi: 10.1016/j.camwa.2016.07.007. |
[13] |
Y. Zhou and L. Peng,
On the time-fractional Navier-Stokes equations, Compu. Math. Appl., 73 (2017), 874-891.
doi: 10.1016/j.camwa.2016.03.026. |
show all references
References:
[1] |
C. Bardos, P. Penel, U. Frisch and P. Sulem,
Modifed dissipativity for a nonlinear evolution equation arising in turbulence, Arch. Ration. Mech. Anal., 71 (1979), 237-256.
doi: 10.1007/BF00280598. |
[2] |
P. M. de Carvalho-Neto and G. Planas,
Mild solutions to the time fractional Navier-stokes equations in $\mathbb{R}^N$, J. Differential Equations, 259 (2015), 2948-2980.
doi: 10.1016/j.jde.2015.04.008. |
[3] |
J. Debbi and M. Dozzi,
On the solution of nonlinear stochastic fractional partial equations in one spatial dimension, Stoch. Proc. Appl., 115 (2005), 1764-1781.
doi: 10.1016/j.spa.2005.06.001. |
[4] |
G. Da. Prato and J. Zabczyk,
Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992. |
[5] |
A. Heibig and L. I. Lalade,
Well-posedness of a linearized fractional derivative fluid model, J. Math. Anal. Appl., 380 (2011), 211-255.
doi: 10.1016/j.jmaa.2011.02.047. |
[6] |
J. Huang, T. Shen and Y. Li,
Dynamics of stochastic fractional Boussinesq equations, Discre. Continu. Dynam. Syst.-B, 20 (2015), 2051-2067.
doi: 10.3934/dcdsb.2015.20.2051. |
[7] |
J. Lions,
Sur l'existence de solution des équation de Navier-Stokes, C. R. Acad. Sci. Pairs, 248 (1959), 2847-2849.
|
[8] |
F. Mainardi,
Fractional Calculus and Waves in Linear Viscoelasticity, Imperrial College Press, London, 2010. |
[9] |
M. Shinbrot,
Fractional derivatives of solutions of the Navier-stokes equations, Arch. Ration. Mech. Anal., 40 (1971), 139-154.
|
[10] |
Y. Wang, J. Xu and P. Kloeden,
Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative, Nonlin. Anal., 135 (2016), 205-222.
doi: 10.1016/j.na.2016.01.020. |
[11] |
C. Zeng and Q. Yang, Mild solution of time fractional Navier-Stokes equations driven by fractional Brownian motion, Preprint, 2017.
doi: 10.1016/j.spa.2017.03.013. |
[12] |
Y. Zhou and L. Peng,
Weak solutions of the time-fractional Navier-Stokes equations and optimal control, Compu. Math. Appl., 73 (2017), 1016-1027.
doi: 10.1016/j.camwa.2016.07.007. |
[13] |
Y. Zhou and L. Peng,
On the time-fractional Navier-Stokes equations, Compu. Math. Appl., 73 (2017), 874-891.
doi: 10.1016/j.camwa.2016.03.026. |
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