Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations

Transactions of the American Mathematical Society

Volumn 355, Issue 12, 2003, Pages 5003-5040

  Bhattacharya, Rabi N ^a   Chen, Larry ^b   Dobson, Scott ^b,c   Guenther, Ronald B ^b   Orum, Chris ^b   Ossiander, Mina ^b   Thomann, Enrique ^b   Waymire, Edward C ^b  

^a University of Arizona   (United States)

^b OREGON STATE UNIVERSITY   (United States)

^c Linn Benton Community College   (United States)

Author keywords

Branching random walk; Feynman Kac; Incompressible Navier Stokes; Multiplicative cascade; Reaction diffusion

Indexed keywords

EID: 0344065857     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03246-X     Document Type: Article

References (23)

1. Albeverio, S. and R. Høegh-Krohn (1976): Mathematical theory of Feynman path integrals, Lecture Notes in Mathematics 523, Springer-Verlag, NY. MR 58:14535
2. Aronszajn, N. and K.T. Smith (1961): Theory of Bessel potentials I, Ann. Inst. Fourier (Grenoble) 11 385-475. MR 26:1485
3. Bhattacharya, R.N. and R.R. Rao (1976): Normal approximation and asymptotic expansions, Wiley, NY. MR 55:9219
4. Cannone, M. and F. Planchon (2000): On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations, Revista Matemática Iberoamericana 16 1-16. MR 2001d:35158
5. 3, Math. Appl. Anal. 2 307-319. MR 96h:35151
6. Chen, Zhi Min and Zhouping Xin (2001): Homogeneity criterion for the Navier-Stokes equations in the whole space, Journal of Mathematical Fluid Mechanics 3 152-182. MR 2002d:76033
7. Chen, L., S. Dobson, R. Guenther, C. Orum, M. Ossiander, E. Waymire (2003): On Itô's complex measure condition, IMS Lecture-Notes Monographs Series, Papers in Honor of Rabi Bhattacharya, eds. K. Athreya, M. Majumdar, M. Puri, E. Waymire 41, 65-80.
8. Feller, W. (1971): An Introduction to Probability Theory and its Applications, vol II, Wiley, NY. MR 42:5292
9. Folland, Gerald B. (1992): Fourier Analysis and its Applications, Brooks/Cole Publishing Company, Pacific Grove, California. MR 93f:42001
10. Foias, C. and R. Temam (1989): Grevey class regularity for the solutions of the Navier-Stokes equations, J. Functional Analysis 87 359-369. MR 91a:35135
11. Fujita, H. and T. Kato (1964): On the Navier-Stokes initial value problem I, Arch. Rational Mech. Anal. 16, 269-315. MR 29:3774
12. Galdi, G.P. (1994): An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Springer-Verlag, NY. MR 91a:35135
13. Harris, T. (1989): The Theory of Branching Processes, Dover Publ. Inc., NY. MR 29:664
14. Itô, K.(1965): Generalized uniform complex measures in the Hilbertian metric space with the application to the Feynman integral, Proc. Fifth Berkeley Symp. Math. Stat. Probab. II, 145-161. MR 35:7359
15. m with applications to weak solutions, Math. Z. 187 471-480. MR 86b:35171
16. 3 C.R. Acad. Sci. Paris, t.330, Série 1, 183-186. MR 2001c:35190
17. LeJan, Y. and A.S. Sznitman (1997): Stochastic cascades and 3-dimensional Navier-Stokes equations, Prob. Theory and Rel. Fields 109 343-366. MR 98j:35144
18. McKean, H.P. (1975): Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov, Comm. Pure. Appl. Math. 28 323-331. MR 53:4262
19. Montgomery-Smith, S. (2001): Finite time blow up for a Navier-Stokes like equation, Proc. A.M.S. 129, 3025-3029. MR 2002d:35164
20. Orum, Chris (2003): Ph.D. Thesis, Oregon State University.
21. Temam, R. (1995): Navier Stokes Equations and Nonlinear Functional Analysis, SIAM, Philadelphia, PA. MR 96e:35136
22. Woyczynski,W., P. Biler, and T. Funaki (1998): Fractal Burgers equations, J. Diff. Equations 148, 9-46. MR 99g:35111
23. Yamazato, M. (1978): Unimodality of infinitely divisible distribution functions of class L, Ann. Probab. 6, no. 4, 523-531. MR 58:2976