Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 2
Submit an article Journal homepage
157
Views
38
CrossRef citations to date
0
Altmetric
Articles

Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz–Morrey spaces

Sadek GalaDepartment of Mathematics, University of Mostaganem, Box 227, 27000, Mostaganem, Algeria.Correspondence[email protected]
,
Maria Alessandra RagusaDipartimento di Mathematica e Informatica, Universit? di Catania, 6, 95125, Viale Andrea Doria, Catania, Italy.
,
Yoshihiro SawanoDepartment of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami Ohsawa, 606-8502,, HachiojiTokyo, Japan.
&
Hitoshi TanakaDepartment of Mathematical Science, The University of Tokyo, 153-8914, Tokyo, Japan.
Pages 356-368 | Received 16 Oct 2012, Accepted 29 Jan 2013, Published online: 04 Mar 2013

References

  • Constantin P, Majda A, Tabak E. Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar. Nonlinearity. 1994;7:1495–1533.
  • Stein EM. Harmonic analysis. Princeton: Princeton University Press; 1993.
  • Pedlosky J. Geophysical fluid dynamics. New York (NY): Springer; 1987.
  • Constantin P, Cordoba D, Wu J. On the critical dissipative quasigeostrophic equation. Indiana University Mathematics Journal. 2001;50:97–107.
  • Ju N. Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equation in the Sobolev space. Communications in Mathematical Physics. 2004;251:365–376.
  • Liu Q, Jia Y, Dong B. Remarks on the weak-strong uniqueness for the 2D quasi-geostrophic equation in BMO space. Applied Mathematics Letters. 2012;25:1470–1474.
  • Marchand F. Weak-strong uniqueness criteria for the critical quasi-geostrophic equation. Physica D. 2008;237:1346–1351.
  • Triebel H. Theory of function spaces. Basel: Birkhauser; 1983.
  • Kozono H, Yamazaki M. Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data. Communications in Partial Differential Equations. 1994;19:959–1014.
  • Wu J. The 2D dissipative quasi-geostrophic equation. Applied Mathematics Letters. 2002;15:925–930.
  • Constantin P, Wu J. Behavior of solutions of 2D quasi-geostrophic equations. SIAM Journal on Mathematical Analysis. 1999;30:937–948.
  • Dong BQ, Chen ZM. Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. Nonlinearity. 2006;19:2919–2928.
  • Sugano S. Some inequalities for generalized fractional integral operators on generalized Morrey spaces and their remarks, Mathematical Inequalities and Applications 14 (2011), 849-865.
  • Gala S, Sawano Y, Tanaka H. A new Beale-Kato-Majda criteria for the 3D magneto-micropolar fluid equations in Orlicz-Morrey spaces. Mathematical Methods in the Applied Sciences. 2012;35:1321–1334.
  • Sawano Y, Sugano S, Tanaka H. A note on generalized fractional integral operators on generalized Morrey spaces. Boundary Value Problems. 2009;2009(Art. ID 835865):18.
  • Bo-Qing D, Zhi-Min C. On the weak-strong uniqueness of the dissipative surface quasi-geostrophic equation. Nonlinearity. 2012;25(5):1513–1524.
  • Sawano Y, Sugano S, Tanaka H. Orlicz-Morrey spaces and fractional operators. Potential Analysis. 2012;36:517–556.
  • Sawano Y, Sugano S, Tanaka H. Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces. Transactions of the American Mathematical Society. 2011;363:6481–6503.
  • Sawano Y, Sugano S, Tanaka H. Olsen’s inequality and its applications to Schrödinger equations. RIMS Kkyroku Bessatsu. 2011;B26:51–80.
  • Pérez C. Sharp Lp-weighted Sobolev inequalities. Annales De L’institut Fourier (Grenoble). 1995;45:809–824.
  • Tanaka H. Morrey spaces and fractional operators. Journal of the Australian Mathematical Society. 2010;88:247–259.
  • Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 1983.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.