Abstract
The results presented in this paper are generalizations of earlier work on the linear stability of non-rotating round gas balls in equilibrium, with respect to perturbations with zero angular momentum. Here we allow a more general barotropic equation of state for the gas, a non-zero angular momentum of the equilibrium state, and we are considering arbitrary numbers of gas balls, intending to use the result later to prove non-linear stability. The result requires an energy stability condition, which we verify for a single, slowly rotating gas ball, and the restricted class of equations of state used in earlier papers.
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References
Friedman A.: Partial Differential Equations. Krieger Malabar, Florida (1983)
Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order, second edition, Springer, Berlin (1983)
Günter N.M.: Potential Theory and its Applications to Basic Problems of Mathematical Physics. Frederick Ungar, New York (1967)
Guo Y., Tice I.: Decay of viscous surface waves without surface tension in horizontally infinite domains, Anal. PDE 6(6), 1429–1533 (2013)
Guo Y., Tice I.: Almost exponential decay of periodic viscous surface waves without surface tension. Arch. Ration. Mech. Anal. 207(2), 459–531 (2013)
Li D., Ströhmer G., Wang L.: Symmetry of integral equations on bounded domains. Proc. AMS 137, 3695–3702 (2009)
Padula M.: Asymptotic Stability of Steady Compressible Fluids. Springer, Heidelberg (2011)
Solonnikov, V. A.: On the stability of uniformly rotating viscous incompressible self-gravitating liquid. (English, Russian summary) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 348 (2007), Kraevye Zadachi Matematicheskoi Fiziki i Smezhnye Voprosy Teorii Funktsii. 38, 165–208, 305 (translation in J. Math. Sci. (N. Y.) 152(5),713–740) (2008)
Ströhmer G., Zajązkowski W.: On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids. Indiana Univ. Math. J. 46, 1181–1220 (1997)
Ströhmer G.: About the linear stability of the spherically symmetric solution for the equations of a barotropic viscous fluid under the influence of self-gravitation. J. Math. Fluid Mech. 8, 36–63 (2006)
Ströhmer G.: About the stability of gas balls. J. Math. Fluid Mech. 11, 572–608 (2009)
Ströhmer G.: Existence and structural stability for certain configurations of rotating barotropic fluids. J. Math. Fluid Mech. 16, 193–210 (2014)
Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam (1978)
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Ströhmer, G. About Linear Stability for Multiple Gas Balls. J. Math. Fluid Mech. 18, 71–88 (2016). https://doi.org/10.1007/s00021-015-0231-8
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DOI: https://doi.org/10.1007/s00021-015-0231-8