American Institute of Mathematical Sciences

Advanced
May  2010, 27(2): 847-861. doi: 10.3934/dcds.2010.27.847

Eventual regularization of the slightly supercritical fractional Burgers equation

Chi Hin Chan 1, , Magdalena Czubak 2, and  Luis Silvestre 3,

1. 

Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street SE, Minneapolis, MN 55455-0134, United States
2. 

Department of Mathematics, University of Toronto, 40 St. George St. Toronto, Ontario, M5S 2E4, Canada
3. 

Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637, United States

Received  October 2009 Revised  February 2010 Published  February 2010

We prove that a weak solution of a slightly supercritical fractional Burgers equation becomes Hölder continuous for large time.
Keywords: Holder, fractal, oscillation, supercritical, De Giorgi., fractional Burgers.
Mathematics Subject Classification: 35D1.
Citation: Chi Hin Chan, Magdalena Czubak, Luis Silvestre. Eventual regularization of the slightly supercritical fractional Burgers equation. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 847-861. doi: 10.3934/dcds.2010.27.847
[1]

Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017
[2]

Changfeng Gui. On some problems related to de Giorgi’s conjecture. Communications on Pure & Applied Analysis, 2003, 2 (1) : 101-106. doi: 10.3934/cpaa.2003.2.101
[3]

Paolo Baroni, Agnese Di Castro, Giampiero Palatucci. Intrinsic geometry and De Giorgi classes for certain anisotropic problems. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 647-659. doi: 10.3934/dcdss.2017032
[4]

Luis A. Caffarelli, Alexis F. Vasseur. The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 409-427. doi: 10.3934/dcdss.2010.3.409
[5]

Fabio Paronetto. A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 853-866. doi: 10.3934/dcdss.2017043
[6]

S. Aaron, Z. Conn, Robert S. Strichartz, H. Yu. Hodge-de Rham theory on fractal graphs and fractals. Communications on Pure & Applied Analysis, 2014, 13 (2) : 903-928. doi: 10.3934/cpaa.2014.13.903
[7]

Zhaosheng Feng, Yu Huang. Approximate solution of the Burgers-Korteweg-de Vries equation. Communications on Pure & Applied Analysis, 2007, 6 (2) : 429-440. doi: 10.3934/cpaa.2007.6.429
[8]

Alexandre Boritchev. Decaying turbulence for the fractional subcritical Burgers equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2229-2249. doi: 10.3934/dcds.2018092
[9]

Binbin Shi, Weike Wang. Existence and blow up of solutions to the $ 2D $ Burgers equation with supercritical dissipation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019215
[10]

Vincent Millot, Yannick Sire, Hui Yu. Minimizing fractional harmonic maps on the real line in the supercritical regime. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6195-6214. doi: 10.3934/dcds.2018266
[11]

Ze Cheng, Changfeng Gui, Yeyao Hu. Existence of solutions to the supercritical Hardy-Littlewood-Sobolev system with fractional Laplacians. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1345-1358. doi: 10.3934/dcds.2019057
[12]

Yan Wang, Guanggan Chen. Invariant measure of stochastic fractional Burgers equation with degenerate noise on a bounded interval. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3121-3135. doi: 10.3934/cpaa.2019140
[13]

Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255
[14]

Chunxiao Guo, Fan Cui, Yongqian Han. Global existence and uniqueness of the solution for the fractional Schrödinger-KdV-Burgers system. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1687-1699. doi: 10.3934/dcdss.2016070
[15]

Ömer Oruç, Alaattin Esen, Fatih Bulut. A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 533-542. doi: 10.3934/dcdss.2019035
[16]

Manuel Fernández-Martínez. Theoretical properties of fractal dimensions for fractal structures. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1113-1128. doi: 10.3934/dcdss.2015.8.1113
[17]

Uta Renata Freiberg. Einstein relation on fractal objects. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 509-525. doi: 10.3934/dcdsb.2012.17.509
[18]

Umberto Mosco, Maria Agostina Vivaldi. Vanishing viscosity for fractal sets. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1207-1235. doi: 10.3934/dcds.2010.28.1207
[19]

Chun-Hsiung Hsia, Xiaoming Wang. On a Burgers' type equation. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1121-1139. doi: 10.3934/dcdsb.2006.6.1121
[20]

Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (16)
  • HTML views (0)
  • Cited by (16)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences