publication . Article . Preprint . 2013

three dimensional steady subsonic euler flows in bounded nozzles

Chao Chen; Chunjing Xie;
Open Access
  • Published: 09 May 2013 Journal: Journal of Differential Equations, volume 256, pages 3,684-3,708 (issn: 0022-0396, Copyright policy)
  • Publisher: Elsevier BV
Abstract The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic–sonic flow. Furthermore, when the normal component of vorticity a...
arXiv: Physics::Fluid Dynamics
free text keywords: Analysis, Euler system, Nonlinear system, Euler's formula, symbols.namesake, symbols, Bernoulli's principle, Potential flow, Momentum, A priori estimate, Mathematical optimization, Vorticity, Mathematical analysis, Mathematics, Mathematics - Analysis of PDEs
Related Organizations
34 references, page 1 of 3

[1] H. D. Alber, Existence of three-dimensional, steady, inviscid, incompressible flows with nonvanishing vorticity, Math. Ann., 292 (1992), pp. 493-528.

[2] L. Bers, Existence and uniqueness of a subsonic flow past a given profile, Comm. Pure Appl. Math., 7 (1954), pp. 441-504. [OpenAIRE]

[3] L. Bers, Mathematical aspects of subsonic and transonic gas dynamics, Surveys in Applied Mathematics, 3, John Wiley & Sons, Inc., New York, 1958.

[4] C. Chen and C. J. Xie, Three dimensional subsonic Euler flows in general domains, preprint, 2013.

[5] C. Chen, L. L. Du and C. J. Xie, Subsonic Euler flows past a bump, preprint, 2012.

[6] Gui-Qiang Chen, Jun Chen, and Mikhail Feldman, Transonic shocks and free boundary problems for the full Euler equations in infinite nozzles, J. Math. Pures Appl., 88 (2007), pp. 191-218.

[7] Gui-Qiang Chen, Jun Chen, and Kyungwoo Song, Transonic nozzle flows and free boundary problems for the full Euler equations, J. Differential Equations, 229(2006), pp. 92-120.

[8] G. Q. Chen, C. Dafermos, M. Slemrod, and D. H. Wang, On two-dimensional sonic-subsonic flow, Comm. Math. Phys., 271 (2007), pp. 635-647. [OpenAIRE]

[9] Jun Chen, Subsonic Euler flows in half plane, J. Hyperbolic Differ. Equ., 6 (2009), pp. 207-228.

[10] Shuxing Chen, Transonic shocks in 3-D compressible flow passing a duct with a general section for Euler systems, Trans. Amer. Math. Soc., 360 (2008), pp. 5265-5289.

[11] Shuxing Chen and Hairong Yuan, Transonic shocks in compressible flow passing a duct for three-dimensional Euler systems, Arch. Ration. Mech. Anal., 187(2008), pp. 523-556. [OpenAIRE]

[12] R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948.

[13] G. C. Dong, Nonlinear partial differential equations of second order, Translations of Mathematical Monographs, 95, American Mathematical Society, Providence, RI, 1991.

[14] Lili Du, Ben Duan, Global subsonic Euler flows in an infinitely long axisymmetric nozzle, J. Differential Equations, 250(2011), pp. 813-847.

[15] Lili Du, Zhouping Xin, Wei Yan, Subsonic flows in a multi-dimensional nozzle, Arch. Rational Mech. Anal., 2011, pp. 965-1012. [OpenAIRE]

34 references, page 1 of 3
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue