THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME*

doi:10.1007/s10473-024-0513-4

Abstract

CLC Number:

35A05

Lin ZHENG, Shu WANG. THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME^*[J].Acta mathematica scientia,Series B, 2024, 44(5): 1877-1885.

Trendmd

References

[1] Carrillo J A, Goudon T. Stability and asymptotic analysis of a fluid-particle interaction model. Commun Partial Differ Equ, 2006, 31: 1349-1379
[2] Berres S, Bürger R, Karlsen K H, et al. Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. SIAM J Appl Math, 2003, 64(1): 41-80
[3] Baranger C, Boudin L, Mancini S. A modeling of biospray for the upper airways. CEMRACS2004 Mathematics and Applications to Biology and Medicine, ESAIM Proc, 2005, 14: 41-47
[4] Vinkovic I, Aguirre C, Simoëns S, et al. Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow. International Journal of Multiphase Flow, 2006, 32: 344-364
[5] Williams F A. Spray combustion and atomization. Phys Fluids, 1958, 1: 541-555
[6] Williams F A. Combustion Theory.2nd ed. Menlo Park, CA: Benjamin Cummings Publ, 1985
[7] Carrillo J A, Karper T, Trivisa K. On the dynamics of a fluid-particle interaction model: the bubbling regime. Nonlinear Anal, 2011, 74: 2778-2801
[8] Fang D Y, Zi R Z, Zhang T. Global classical large solutions to a 1D fluid-particle interaction model: The bubbling regime. J Math Phys, 2012, 53(3): 41-80
[9] Song Y K, Yuan H J, Chen Y, et al. Strong solutions to a 1D fluid-particle interaction non-newtonian model: The bubbling regime. J Math Phys, 2013, 54(9): 41-80
[10] Ballew J, K Trivisa. Weakly dissipative solutions and weak-strong uniqueness for the Navier Stokes Smolunchowski system. Nonlinear Analysis Series A: Theory, Methods Applications, 2013, 91: 1-19
[11] Ballew J. Low Mach number limits to the Navier Stokes Smolunchowski system. Hyperbolic Problems: Theory, Numerics, Applications. AIMS Series on Applied Mathematics, 2014, 8: 301-308
[12] Huang B Y, Ding S J, Wen H Y. Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum. Discret Contin Dyn Syst, 2016, 9(6): 1717-1752
[13] Chen Y S, Ding S J, Wang W J. Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations. Discret Contin Dyn Syst, 2016, 36: 5287-5307
[14] Ding S J, Huang B Y, Wen H Y. Global well-posedness of classicial solutions to a fluid-particle interaction model in $\mathbb{R}^3$. J Diff Eqns, 2017, 263: 8666-8717
[15] Matsumura A, Nishida T. Initial boundary problems for the equations of motion of compressible viscous and heat-conducive fluids. Commun Math Phys, 1983, 89: 445-464
[16] Zheng L, Wang S, Li L R. Local classical solutions of 3D fluid-particle interaction model: the flowing regimen. Acta Math Sci, 2018, 38A(6): 1173-1192

THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME^*

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Hao Wang. GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION [J]. Acta mathematica scientia,Series B, 2024, 44(4): 1347-1372.
[2]	Weiyuan Zou. THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES QUATIONS IN THE WHOLE DOMAIN [J]. Acta mathematica scientia,Series B, 2024, 44(3): 887-908.
[3]	Mingxuan Zhu, Zaihong Jiang. THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION^* [J]. Acta mathematica scientia,Series B, 2023, 43(2): 736-750.
[4]	Boling Guo, Yamin Xiao. THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM^* [J]. Acta mathematica scientia,Series B, 2023, 43(2): 942-958.
[5]	Quansen Jiu, Lin Ma. GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^* [J]. Acta mathematica scientia,Series B, 2023, 43(1): 25-42.
[6]	Wenjun WANG, Zhen CHENG. LARGE TIME BEHAVIOR OF GLOBAL STRONG SOLUTIONS TO A TWO-PHASE MODEL WITH A MAGNETIC FIELD [J]. Acta mathematica scientia,Series B, 2022, 42(5): 1921-1946.
[7]	Bingyuan HUANG, Shijin DING, Riqing WU. CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD [J]. Acta mathematica scientia,Series B, 2022, 42(4): 1585-1606.
[8]	Ruiying WEI, Yin LI, Zheng-an YAO. THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL [J]. Acta mathematica scientia,Series B, 2022, 42(3): 1058-1080.
[9]	Jianjun HUANG, Zhenglu JIANG. GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS [J]. Acta mathematica scientia,Series B, 2020, 40(5): 1335-1351.
[10]	Lamia DJEBARA, Salem ABDELMALEK, Samir BENDOUKHA. GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR SOME COUPLED SYSTEMS VIA A LYAPUNOV FUNCTIONAL [J]. Acta mathematica scientia,Series B, 2019, 39(6): 1538-1550.
[11]	Zhensheng GAO, Yan LIANG, Zhong TAN. A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK [J]. Acta mathematica scientia,Series B, 2019, 39(6): 1639-1660.
[12]	Hua CHEN, Huiyang XU. GLOBAL EXISTENCE, EXPONENTIAL DECAY AND BLOW-UP IN FINITE TIME FOR A CLASS OF FINITELY DEGENERATE SEMILINEAR PARABOLIC EQUATIONS [J]. Acta mathematica scientia,Series B, 2019, 39(5): 1290-1308.
[13]	Yuzhu WANG, Naiwen TIAN. ON THE CAUCHY PROBLEM FOR IMBQ SYSTEM ARISING FROM DNA [J]. Acta mathematica scientia,Series B, 2019, 39(4): 1136-1148.
[14]	Yingshu ZHANG, Lang LI, Shaomei FANG. GLOBAL EXISTENCE AND POINTWISE ESTIMATES OF SOLUTIONS TO GENERALIZED KURAMOTO-SIVASHINSKY SYSTEM IN MULTI-DIMENSIONS [J]. Acta mathematica scientia,Series B, 2019, 39(1): 180-194.
[15]	Dexing KONG, Qi LIU. GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION [J]. Acta mathematica scientia,Series B, 2018, 38(3): 745-755.