-
Previous Article
Periodic solutions of El Niño model through the Vallis differential system
- DCDS Home
- This Issue
-
Next Article
Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension
On a generalized maximum principle for a transport-diffusion model with $\log$-modulated fractional dissipation
1. | Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912 |
2. | Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 |
References:
[1] |
R. Askey, Radial Characteristic Functions, University of Wisconsin-Madison, Mathematics Research Center, 1262, 1973. |
[2] |
A. Córdoba and D. Córdoba, A maximum principle applied to quasi-geostrophic equations, Comm. Math. Phys., 249 (2004), 511-528.
doi: 10.1007/s00220-004-1055-1. |
[3] |
C. H. Chan, M. Czubak and L. Silvestre, Eventual regularization of the slightly supercritical fractional Burgers equation, Discrete Contin. Dyn. Syst., 27 (2010), 847-861.
doi: 10.3934/dcds.2010.27.847. |
[4] |
H. Dong, D. Du and D. Li, Finite time singularities and global well-posedness for fractal Burgers equations, Indiana Univ. Math. J., 58 (2009), 807-821.
doi: 10.1512/iumj.2009.58.3505. |
[5] |
M. Dabkowski, A. Kiselev, L. Silvestre and V. Vicol, Global well-posedness of slightly supercritical active scalar equations,, Analysis and PDE, ().
|
[6] |
M. Dabkowski, A. Kiselev and V. Vicol, Global well-posedness for a slightly supercritical surface quasi-geostrophic equation, Nonlinearity, 25 (2012), 1525-1535.
doi: 10.1088/0951-7715/25/5/1525. |
[7] |
T. Hmidi, On a maximum principle and its application to the logarithmically critical Boussinesq system, Anal. PDE, 4 (2011), 247-284.
doi: 10.2140/apde.2011.4.247. |
[8] |
N. Ju, The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations, Comm. Math. Phys., 255 (2005), 161-181.
doi: 10.1007/s00220-004-1256-7. |
[9] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970. |
[10] |
T. Tao, Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation, Anal. PDE, 2 (2009), 361-366.
doi: 10.2140/apde.2009.2.361. |
[11] |
J. Wu, Global regularity for a class of generalized magnetohydrodynamic equations, J. Math. Fluid Mech., 13 (2011), 295-305.
doi: 10.1007/s00021-009-0017-y. |
show all references
References:
[1] |
R. Askey, Radial Characteristic Functions, University of Wisconsin-Madison, Mathematics Research Center, 1262, 1973. |
[2] |
A. Córdoba and D. Córdoba, A maximum principle applied to quasi-geostrophic equations, Comm. Math. Phys., 249 (2004), 511-528.
doi: 10.1007/s00220-004-1055-1. |
[3] |
C. H. Chan, M. Czubak and L. Silvestre, Eventual regularization of the slightly supercritical fractional Burgers equation, Discrete Contin. Dyn. Syst., 27 (2010), 847-861.
doi: 10.3934/dcds.2010.27.847. |
[4] |
H. Dong, D. Du and D. Li, Finite time singularities and global well-posedness for fractal Burgers equations, Indiana Univ. Math. J., 58 (2009), 807-821.
doi: 10.1512/iumj.2009.58.3505. |
[5] |
M. Dabkowski, A. Kiselev, L. Silvestre and V. Vicol, Global well-posedness of slightly supercritical active scalar equations,, Analysis and PDE, ().
|
[6] |
M. Dabkowski, A. Kiselev and V. Vicol, Global well-posedness for a slightly supercritical surface quasi-geostrophic equation, Nonlinearity, 25 (2012), 1525-1535.
doi: 10.1088/0951-7715/25/5/1525. |
[7] |
T. Hmidi, On a maximum principle and its application to the logarithmically critical Boussinesq system, Anal. PDE, 4 (2011), 247-284.
doi: 10.2140/apde.2011.4.247. |
[8] |
N. Ju, The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations, Comm. Math. Phys., 255 (2005), 161-181.
doi: 10.1007/s00220-004-1256-7. |
[9] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970. |
[10] |
T. Tao, Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation, Anal. PDE, 2 (2009), 361-366.
doi: 10.2140/apde.2009.2.361. |
[11] |
J. Wu, Global regularity for a class of generalized magnetohydrodynamic equations, J. Math. Fluid Mech., 13 (2011), 295-305.
doi: 10.1007/s00021-009-0017-y. |
[1] |
Siwei Duo, Hong Wang, Yanzhi Zhang. A comparative study on nonlocal diffusion operators related to the fractional Laplacian. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 231-256. doi: 10.3934/dcdsb.2018110 |
[2] |
Martin Burger, Jan-Frederik Pietschmann, Marie-Therese Wolfram. Identification of nonlinearities in transport-diffusion models of crowded motion. Inverse Problems and Imaging, 2013, 7 (4) : 1157-1182. doi: 10.3934/ipi.2013.7.1157 |
[3] |
Vincenzo Ambrosio, Giovanni Molica Bisci. Periodic solutions for nonlocal fractional equations. Communications on Pure and Applied Analysis, 2017, 16 (1) : 331-344. doi: 10.3934/cpaa.2017016 |
[4] |
Yunkyong Hyon, Do Young Kwak, Chun Liu. Energetic variational approach in complex fluids: Maximum dissipation principle. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1291-1304. doi: 10.3934/dcds.2010.26.1291 |
[5] |
Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153 |
[6] |
Gernot Holler, Karl Kunisch. Learning nonlocal regularization operators. Mathematical Control and Related Fields, 2022, 12 (1) : 81-114. doi: 10.3934/mcrf.2021003 |
[7] |
Matthieu Alfaro, Jérôme Coville, Gaël Raoul. Bistable travelling waves for nonlocal reaction diffusion equations. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1775-1791. doi: 10.3934/dcds.2014.34.1775 |
[8] |
Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure and Applied Analysis, 2005, 4 (4) : 735-742. doi: 10.3934/cpaa.2005.4.735 |
[9] |
Patrizia Pucci, Mingqi Xiang, Binlin Zhang. A diffusion problem of Kirchhoff type involving the nonlocal fractional p-Laplacian. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 4035-4051. doi: 10.3934/dcds.2017171 |
[10] |
Liang Zhang, X. H. Tang, Yi Chen. Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators. Communications on Pure and Applied Analysis, 2017, 16 (3) : 823-842. doi: 10.3934/cpaa.2017039 |
[11] |
M. Euler, N. Euler, M. C. Nucci. On nonlocal symmetries generated by recursion operators: Second-order evolution equations. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4239-4247. doi: 10.3934/dcds.2017181 |
[12] |
Isabeau Birindelli, Francoise Demengel. Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators. Communications on Pure and Applied Analysis, 2007, 6 (2) : 335-366. doi: 10.3934/cpaa.2007.6.335 |
[13] |
Martin Frank, Weiran Sun. Fractional diffusion limits of non-classical transport equations. Kinetic and Related Models, 2018, 11 (6) : 1503-1526. doi: 10.3934/krm.2018059 |
[14] |
Nguyen Anh Tuan, Donal O'Regan, Dumitru Baleanu, Nguyen H. Tuan. On time fractional pseudo-parabolic equations with nonlocal integral conditions. Evolution Equations and Control Theory, 2022, 11 (1) : 225-238. doi: 10.3934/eect.2020109 |
[15] |
Nikolaos Roidos, Yuanzhen Shao. Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation. Evolution Equations and Control Theory, 2022, 11 (3) : 793-825. doi: 10.3934/eect.2021026 |
[16] |
Marco Di Francesco, Yahya Jaafra. Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion. Kinetic and Related Models, 2019, 12 (2) : 303-322. doi: 10.3934/krm.2019013 |
[17] |
Dinh-Ke Tran, Tran-Phuong-Thuy Lam. Nonlocal final value problem governed by semilinear anomalous diffusion equations. Evolution Equations and Control Theory, 2020, 9 (3) : 891-914. doi: 10.3934/eect.2020038 |
[18] |
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar. On the local and global existence of solutions to 1d transport equations with nonlocal velocity. Networks and Heterogeneous Media, 2019, 14 (3) : 471-487. doi: 10.3934/nhm.2019019 |
[19] |
Lijuan Wang, Weike Wang. Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2835-2854. doi: 10.3934/cpaa.2019127 |
[20] |
Dong Li, Xiaoyi Zhang. On a nonlocal aggregation model with nonlinear diffusion. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 301-323. doi: 10.3934/dcds.2010.27.301 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]