-
Previous Article
Cell death and the maintenance of immunological memory
- DCDS-B Home
- This Issue
-
Next Article
A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis
Structure of 2D incompressible flows with the Dirichlet boundary conditions
1. | Department of Mathematics, Sichuan University, Chengdu |
2. | Department of Mathematics, Indiana University, Bloomington, IN 47405 |
The main motivation of this article is to provide an important step for a forthcoming paper, where, for the first time, we are able to establish precise rigorous criteria on boundary layer separations of incompressible fluid flows, a long standing problem in fluid mechanics.
[1] |
Hitoshi Ishii, Taiga Kumagai. Averaging of Hamilton-Jacobi equations along divergence-free vector fields. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1519-1542. doi: 10.3934/dcds.2020329 |
[2] |
Jaume Llibre, Jesús S. Pérez del Río, J. Angel Rodríguez. Structural stability of planar semi-homogeneous polynomial vector fields applications to critical points and to infinity. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 809-828. doi: 10.3934/dcds.2000.6.809 |
[3] |
Lev M. Lerman, Elena V. Gubina. Nonautonomous gradient-like vector fields on the circle: Classification, structural stability and autonomization. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1341-1367. doi: 10.3934/dcdss.2020076 |
[4] |
Livio Flaminio, Miguel Paternain. Linearization of cohomology-free vector fields. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1031-1039. doi: 10.3934/dcds.2011.29.1031 |
[5] |
Hugo Beirão da Veiga. A challenging open problem: The inviscid limit under slip-type boundary conditions.. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 231-236. doi: 10.3934/dcdss.2010.3.231 |
[6] |
José M. Arrieta, Simone M. Bruschi. Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 327-351. doi: 10.3934/dcdsb.2010.14.327 |
[7] |
Catherine Lebiedzik. Uniform stability in a vectorial full Von Kármán thermoelastic system with solenoidal dissipation and free boundary conditions. Evolution Equations and Control Theory, 2021, 10 (4) : 767-796. doi: 10.3934/eect.2020092 |
[8] |
Pierre-Étienne Druet. Higher $L^p$ regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some low-frequency Maxwell equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 475-496. doi: 10.3934/dcdss.2015.8.475 |
[9] |
Micol Amar. A note on boundary layer effects in periodic homogenization with Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 537-556. doi: 10.3934/dcds.2000.6.537 |
[10] |
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci. Classification of irregular free boundary points for non-divergence type equations with discontinuous coefficients. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6073-6090. doi: 10.3934/dcds.2018262 |
[11] |
Aram L. Karakhanyan. Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 261-277. doi: 10.3934/dcds.2016.36.261 |
[12] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1047-1069. doi: 10.3934/dcds.2008.21.1047 |
[13] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[14] |
Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez. Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets. Conference Publications, 2007, 2007 (Special) : 181-190. doi: 10.3934/proc.2007.2007.181 |
[15] |
Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1205-1235. doi: 10.3934/dcds.2019052 |
[16] |
Le Thi Phuong Ngoc, Khong Thi Thao Uyen, Nguyen Huu Nhan, Nguyen Thanh Long. On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions. Communications on Pure and Applied Analysis, 2022, 21 (2) : 585-623. doi: 10.3934/cpaa.2021190 |
[17] |
Kehan Shi, Ying Wen. Nonlocal biharmonic evolution equations with Dirichlet and Navier boundary conditions. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022089 |
[18] |
Huiqiang Jiang. Regularity of a vector valued two phase free boundary problems. Conference Publications, 2013, 2013 (special) : 365-374. doi: 10.3934/proc.2013.2013.365 |
[19] |
Reuven Segev, Lior Falach. The co-divergence of vector valued currents. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 687-698. doi: 10.3934/dcdsb.2012.17.687 |
[20] |
Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Kinematical structural stability. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 529-536. doi: 10.3934/dcdss.2016010 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]