Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space

By Ning Ju. 2004

243 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f50c54ac8c9bc9d6a9e2a3921d66fe753df99d50

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Vlad Vicol
2. Peter Constantin
3. Changxing Miao
4. Taoufik Hmidi
5. Andrej Zlatoš
6. Sahbi Keraani
7. Jiahong Wu
8. Andrea L. Bertozzi

In Control and Systems Engineering

1. Peter Constantin
2. Changxing Miao
3. Vlad Vicol
4. Taoufik Hmidi
5. Hideyuki Miura
6. Sahbi Keraani
7. Maria E. Schonbek
8. César J. Niche

In Mathematical Physics

1. Vlad Vicol
2. Changxing Miao
3. Peter Constantin
4. Taoufik Hmidi
5. Sahbi Keraani
6. Andrej Zlatoš
7. Hideyuki Miura
8. Jiahong Wu

Citations in the corpus

• Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation (2006, background): “Besides the ones we have already referred to, see Berselli [1], Carrillo and Ferreira [4], Chae [7], Chae and Lee [8], Constantin, Córdoba and Wu [9], Ju [14], [16], Schonbek and Schonbek [24], [25], Wu [27], [28], [29], [30], [31], [32] and references contained therein.”
• Long Time Dynamics of Forced Critical SQG (2013, background): “APPENDIX A. FRACTIONAL INEQUALITIES We recall the following fractional product (Kato-Ponce), commutator (Kenig-Ponce-Vega), and Sobolev estimates, cf. [KP88, KPV91, Tay91, SS03, Ju04] and references therein.”
• Finite-Time Blow-up of Solutions of an Aggregation Equation in Rn (2007, background): “The 2D-quasi-geostrophic equations also pose an interesting family of active scalar equations [9, 17 ].”
• Finite time singularity for the modified SQG patch equation (2016, background): “[30]), while in the super-critical case β < 1 2 the question of global regularity vs finite time blow-up remains open.”
• The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations (2005, methodology): “See, among others, Berselli, [2] Chae and Lee [3], Constantin, D. Cordoba and Wu [4], Constantin, Majda and Tabak [7], Constantin and Wu [8], D. Cordoba [9], A. Cordoba and D. Cordoba [10, 11], D. Cordoba and Fefferman [12], Ju [16], Ju [ 17 ], Majda and Tabak [22], Ohkitani et al [23], Resnick [25]”
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces (2006, background): “Ju [12] for small initial data in H with s 2 − α.”
• Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space (2006, methodology): “Ju [9, 10] improved the admissible exponent up to s > 2 − 2α.”
• A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation (2006, background): “In the case (p, q) = (2, 2) , it corresponds to the result of Ning[17] in the Sobolev space H2−2α.”
• A survey of useful inequalities in fractional calculus (2017, unknown): “This inequality has been generalized by Ju [25] as follows.”