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On the constants in a Kato inequality for the Euler and Navier-Stokes equations
1. | Dipartimento di Matematica, Politecnico di Milano, P.za L. da Vinci 32, I-20133 Milano, Italy |
2. | Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133 Milano, Italy |
References:
[1] |
A. Abdelrazec and D. Pelinovsky, Convergence of the Adomian decomposition method for initial-value problems, Numer. Methods Partial Differential Equations 27 (2011), 749-766.
doi: 10.1002/num.20549. |
[2] |
R. A. Adams, "Sobolev Spaces,'' Academic Press, Boston, 1978. |
[3] |
M. V. Bartuccelli, K. B. Blyuss and Y. N. Kyrychko, Length scales and positivity of solutions of a class of reaction-diffusion equations, Comm. Pure Appl. Anal., 3 (2004), 25-40.
doi: 10.3934/cpaa.2004.3.25. |
[4] |
S. I. Chernyshenko, P. Constantin, J. C. Robinson and E. S. Titi, A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations, J. Math. Phys., 48 (2007), 065204/10.
doi: 10.1063/1.2372512. |
[5] |
P. Constantin and C. Foias, "Navier Stokes Equations,'' Chicago University Press, 1988. |
[6] |
T. Kato, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal., 9 (1972), 296-305. |
[7] |
Y. N. Kyrychko and M. V. Bartuccelli, Length scales for the Navier-Stokes equations on a rotating sphere, Phys. Lett. A, 324 (2004), 179-184.
doi: 10.1016/j.physleta.2004.03.008. |
[8] |
C. Morosi and L. Pizzocchero, On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations, Rev. Math. Phys., 20 (2008), 625-706.
doi: 10.1142/S0129055X08003407. |
[9] |
C. Morosi and L. Pizzocchero, An $H^1$ setting for the Navier-Stokes equations: quantitative estimates, Nonlinear Analysis, 74 (2011), 2398-2414.
doi: 10.1016/j.na.2010.11.043. |
[10] |
C. Morosi and L. Pizzocchero, On the constants in a basic inequality for the Euler and Navier-Stokes equations,, preprint, ().
|
[11] |
C. Morosi and L. Pizzocchero, On approximate solutions of the incompressible Euler and Navier-Stokes equations,, preprint, ().
|
[12] |
D. Pelinovsky and A. Sakovich, Global well-posedness of the short-pulse and sine-Gordon equations in energy space, Comm. Partial Differential Equations, 35 (2010), 613-629.
doi: 10.1080/03605300903509104. |
[13] |
P. Zgliczyński and K. Mischaikow, Rigorous numerics for partial differential equations: the Kuramoto-Sivashinsky equation, Found. Comput. Math., 1 (2001), 255-288.
doi: 10.1007/s102080010010. |
[14] |
P. Zgliczyński, Rigorous numerics for dissipative partial differential equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - A computer-assisted proof, Found. Comput. Math., 4 (2004), 157-185.
doi: 10.1007/s10208-002-0080-8. |
show all references
References:
[1] |
A. Abdelrazec and D. Pelinovsky, Convergence of the Adomian decomposition method for initial-value problems, Numer. Methods Partial Differential Equations 27 (2011), 749-766.
doi: 10.1002/num.20549. |
[2] |
R. A. Adams, "Sobolev Spaces,'' Academic Press, Boston, 1978. |
[3] |
M. V. Bartuccelli, K. B. Blyuss and Y. N. Kyrychko, Length scales and positivity of solutions of a class of reaction-diffusion equations, Comm. Pure Appl. Anal., 3 (2004), 25-40.
doi: 10.3934/cpaa.2004.3.25. |
[4] |
S. I. Chernyshenko, P. Constantin, J. C. Robinson and E. S. Titi, A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations, J. Math. Phys., 48 (2007), 065204/10.
doi: 10.1063/1.2372512. |
[5] |
P. Constantin and C. Foias, "Navier Stokes Equations,'' Chicago University Press, 1988. |
[6] |
T. Kato, Nonstationary flows of viscous and ideal fluids in $R^3$, J. Funct. Anal., 9 (1972), 296-305. |
[7] |
Y. N. Kyrychko and M. V. Bartuccelli, Length scales for the Navier-Stokes equations on a rotating sphere, Phys. Lett. A, 324 (2004), 179-184.
doi: 10.1016/j.physleta.2004.03.008. |
[8] |
C. Morosi and L. Pizzocchero, On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations, Rev. Math. Phys., 20 (2008), 625-706.
doi: 10.1142/S0129055X08003407. |
[9] |
C. Morosi and L. Pizzocchero, An $H^1$ setting for the Navier-Stokes equations: quantitative estimates, Nonlinear Analysis, 74 (2011), 2398-2414.
doi: 10.1016/j.na.2010.11.043. |
[10] |
C. Morosi and L. Pizzocchero, On the constants in a basic inequality for the Euler and Navier-Stokes equations,, preprint, ().
|
[11] |
C. Morosi and L. Pizzocchero, On approximate solutions of the incompressible Euler and Navier-Stokes equations,, preprint, ().
|
[12] |
D. Pelinovsky and A. Sakovich, Global well-posedness of the short-pulse and sine-Gordon equations in energy space, Comm. Partial Differential Equations, 35 (2010), 613-629.
doi: 10.1080/03605300903509104. |
[13] |
P. Zgliczyński and K. Mischaikow, Rigorous numerics for partial differential equations: the Kuramoto-Sivashinsky equation, Found. Comput. Math., 1 (2001), 255-288.
doi: 10.1007/s102080010010. |
[14] |
P. Zgliczyński, Rigorous numerics for dissipative partial differential equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - A computer-assisted proof, Found. Comput. Math., 4 (2004), 157-185.
doi: 10.1007/s10208-002-0080-8. |
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