On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface

 Access to full text

 Full (PDF)

1. [1] O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian). 
2. [2] L. Landau and E. Lifschitz, Mechanics of Continuum Media, Nauka, Moscow, 1984; new edition: Hydrodynamics, Nauka, Moscow, 1986 (in Russian). 
3. [3] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104. Zbl0429.76040
4. [4] A. Matsumura and T. Nishida, The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A 55 (1979), 337-342. Zbl0447.76053
5. [5] A. Matsumura and T. Nishida, The initial boundary value problem for the equations of motion of compressible viscous and heat-conductive fluid, preprint Univ. of Wisconsin, MRC Technical Summary Report 2237 (1981). Zbl0543.76099
6. [6] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of general fluids, in: Computing Methods in Applied Sciences and Engineering, R. Glowinski and J. L. Lions (eds.), North-Holland, Amsterdam, 1982, 389-406. Zbl0505.76083
7. [7] A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids, Comm. Math. Phys. 89 (1983), 445-464. Zbl0543.76099
8. [8] K. Pileckas and W. M. Zajączkowski, On free boundary problem for stationary compressible Navier-Stokes equations, Comm. Math. Phys. 128 (1990), 1-36. 
9. [9] V. A. Solonnikov and A. Tani, Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid, preprint of Paderborn University. Zbl0786.35106
10. [10] A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Scuola Norm. Sup. Pisa (4) 10 (1983), 607-647. Zbl0542.35062
11. [11] A. Valli and W. M. Zajączkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case, Comm. Math. Phys. 103 (1986), 259-296. Zbl0611.76082
12. [12] E. Zadrzyńska and W. M. Zajączkowski, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface, Ann. Polon. Math. 59 (1994), 133-170. Zbl0812.35102
13. [13] E. Zadrzyńska and W. M. Zajączkowski, On global motion of a compressible heat conducting fluid bounded by a free surface, Acta Appl. Math. 37 (1994), 221-231. Zbl0813.35130
14. [14] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting fluids, Bull. Polish Acad. Sci. Tech. Sci. 42 (1994), 195-205. Zbl0814.76075
15. [15] E. Zadrzyńska and W. M. Zajączkowski, Conservation laws in free boundary problems for viscous compressible heat conducting capillary fluids, Bull. Polish Acad. Sci. Tech. Sci. 43 (1995), 423-444. Zbl0880.76065
16. [16] E. Zadrzyńska and W. M. Zajączkowski, On a differential inequality for a viscous compressible heat conducting fluid bounded by a free surface, Ann. Polon. Math. 61 (1995), 141-188. Zbl0833.35156
17. [17] E. Zadrzyńska and W. M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, Ann. Polon. Math. 63 (1996), 199-221. Zbl0862.35147
18. [18] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993). Zbl0771.76059
19. [19] W. M. Zajączkowski, On Nonstationary Motion of A Compressible Barotropic Viscous Capillary Fluid Bounded By A Free Surface, Siam J. Math. Anal. 25 (1994), 1-84. Zbl0813.35086

1. Ewa Zadrzyńska, On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary