Mahir Hadžić

Publications

1. (with Christopher Alexander and Matthew Schrecker) Supersonic Gravitational Collapse for Non-Isentropic Gaseous Stars.
   arXiv:2311.18795 , 43 pages (2023)

2. (with Gerhard Rein, Matthew Schrecker and Christopher Straub) Damping versus oscillations for a gravitational Vlasov-Poisson system.
   arXiv:2301.07662 , 49 pages (2023)

3. (with Juhi Jang and King Ming Lam) Nonradial stability of self-similarly expanding Goldreich-Weber stars.
   arXiv:2212.11420 , 64 pages (2022)

4. Star dynamics: Collapse vs. expansion.
   Quarterly of Applied Math., 81 , 329-365 (2023)
   arXiv:2306.02445

5. (with Yan Guo and Juhi Jang) Naked singularities in the Einstein-Euler system.
   Accepted, Annals of PDE
   arXiv:2112.10826 , 150 pages

6. (with Yan Guo, Juhi Jang, and Matthew Schrecker) Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions.
   Archive Rat. Mech. Anal., 246, 957-1066 (2022)
   arXiv:2107.12056
   

7. (with Gerhard Rein and Christopher Straub) On the existence of linearly oscillating galaxies.
   Arch. Rat. Mech. Anal. (2021)
   arXiv:2102.11672 , 104 pages
   

8. (with Yan Guo and Juhi Jang) Larson-Penston Self-similar Gravitational Collapse.
   Commun. Math. Phys., 386, 1551-1601 (2021)
   arXiv:2011.01013

9. (with Zhiwu Lin) Turning point principle for relativistic stars.
   Commun. Math. Phys. 387 (2), 729-759 (2021), Online published version
   arXiv:2006.09749 , 33 pages

10. (with Calum Rickard and Juhi Jang) Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state.
    Nonlinearity, 34(1), 33-91 (2021)
    arXiv:1907.01065
    

11. (with Shrish Parmeshwar and Juhi Jang) Global expanding solutions of compressible Euler equations with small initial densities.
    Quart. Appl. Math., 79 , 273-334 (2021)
    arXiv:1904.01122
    

12. (with Yan Guo and Juhi Jang) Continued gravitational collapse for Newtonian stars.
    Arch. Rat. Mech. Anal. 239 , 431-552 (2021)
    arXiv:1811.01616
    

13. (with Zhiwu Lin and Gerhard Rein) Stability and instability of self-gravitating relativistic matter distributions.
    Arch. Rat. Mech. Anal., 241 , 1-89 (2021)
    arXiv:1810.00809 (the latest Arxiv version fixes a small inconsistency in the proof of Lemma 4.4)
    

14. (with Juhi Jang) A class of global solutions to the Euler-Poisson system.
    Commun. Math. Phys., 370, no 2, 475-505 (2019)
    arXiv:1712.00124

15. (with Juhi Jang) Expanding large global solutions of the equations of compressible fluid mechanics.
    Inventiones Math., 214, no. 3, 1205-1266 (2018)
    arXiv:1610.01666

16. (with Andreas Seeger, Charles Smart, and Brian Street) Singular integrals and a problem on mixing flows.
    Ann. Inst. H. Poincare Anal. Non Lineaire 35, no. 4, 921-943 (2018)
    arXiv:1612.03431
    

17. (with Juhi Jang) Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system.
    Comm. Pure Appl. Math. 71, no. 5, 827-891 (2018)
    arXiv:1605.08083
    

18. (with Gustavo Navarro and Steve Shkoller) Local well-posedness and Global stability of the Two-Phase Stefan problem.
    SIAM J. Math. Anal., 49 6, 4942-5006 (2017)
    arXiv:1607.00681

19. (with Steve Shkoller and Jared Speck) A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary.
    Comm. PDE, 44, 859-906, (2019)
    arXiv:1511.07467

20. (with Pierre Raphael) On melting and freezing for the 2d radial Stefan problem.
    Jour. Eur. Math. Soc., 21, Issue 11, 3259-3341 (2019)
    arXiv:1508.02920

21. (with Steve Shkoller) Global stability and decay for the classical Stefan problem for general boundary shapes.
    Philosophical Transactions of Royal Society A, 373, 2050 (2015)
    arXiv:1501.00463

22. (with Gerhard Rein) On the small redshift limit of steady states of the spherically symmetric Einstein-Vlasov system and their stability.
    Math. Proc. Camb. Phil. Soc. 159, 529-546 (2015)
    arXiv:1407.4649

23. (with Jared Speck) The Global Future Stability of the FLRW Solutions to the Dust-Einstein System with a Positive Cosmological Constant.
    Jour. Hyp. Diff. Eqns.,12, no.1 (2015), 87--188
    arXiv:1309.3502

24. (with Steve Shkoller) Global stability and decay for the classical Stefan problem.
    Comm. Pure Appl. Math., 68 (2015) 689--757
    arXiv:1212.1422

25. (with Gerhard Rein) Stability for the spherically symmetric Einstein-Vlasov system - a coercivity estimate.
    Math. Proc. Camb. Phil. Soc., 155, 529-556 (2013)
    arXiv:1205.6198
    

26. (with Steve Shkoller) Well-posedness for the classical Stefan problem and the zero surface tension limit.
    Arch. Rational Mech. Anal., 1-52, DOI: 10.1007/s00205-016-1041-8
    arXiv:1112.5817

27. Orthogonality conditions and stability in the Stefan problem with surface tension.
    Arch. Rational Mech. Anal., 203 (3), 719-745 (2012)
    arXiv:1101.5177

28. (with Govind Menon) Gradient flow structure for domain relaxation in Langmuir films.
    Quart. Appl. Math., 70, 659-664, (2012)
    arXiv:1009.0226

29. (with Yan Guo) Stability in the Stefan problem with surface tension (I).
    Commun. Partial Differential Eqns. 35 (2), 201-244 (2010)
    arXiv:0801.1083v1

30. (with Gerhard Rein) Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the gravitational case.
    Indiana Univ. Math. J. 56, 2453-2488 (2007)
    The original publication is available here.
    arXiv:math-ph/0607012v1

31. A constraint variational problem arising in stellar dynamics.
    Quart. Appl. Math. 65, 145-153 (2007)
    arXiv:math-ph/0603025v1

Proceedings

1. (with Juhi Jang) Gravitational Collapse for Newtonian Stars.
   Research Institute for Mathematical Science, Kyoto (2022)

2. (with Juhi Jang) Dynamics of expanding gases.
   Research Institute for Mathematical Science, Kyoto, K??ky??roku, No. 2038,
   Mathematical Analysis in Fluid and Gas Dynamics (2017)