Dissipative martingale solutions of the stochastically forced Navier–Stokes–Poisson system on domains without boundary |
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| Institution: | 1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, I–00161, Roma, Italy;2. Institute of Complex Molecular Systems and Faculty of Chemical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;3. Department of Mathematics and Computer Science, (CASA) Centre for Analysis, Scientific Computing and Applications, Institute for Complex Molecular Systems Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;4. Indian Institute of Technology Delhi, India;1. Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 - CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil;2. Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP, Brazil;1. Dipartimento di Scienze di Base e Applicate per l''Ingegneria, Università di Roma “La Sapienza”, via A. Scarpa 16, 00161 Roma, Italy;2. Gran Sasso Science Institute, Viale F. Crispi 7, 00167 L''Aquila, Italy;3. Department of Mathematics and Computer Science, CASA – Center for Scientific Computing and Applications, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands |
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| Abstract: | We construct solutions to the randomly-forced Navier–Stokes–Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense of probability. As such, they satisfy the system in the sense of distributions and the underlying probability space and the stochastic driving force are also unknowns of the problem. Additionally, these solutions dissipate energy, satisfies a relative energy inequality in the sense of Dafermos (1979) and satisfy a renormalized form of the continuity equation in the sense of DiPerna and Lions (1989). |
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| Keywords: | Stochastic compressible fluid Navier–Stokes–Poisson system Weak martingale solution |
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