On the interior regularity criteria for the viscoelastic fluid system with damping

References

[1] L. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math. 35 (1982), no. 6, 771–831. 10.1002/cpa.3160350604Suche in Google Scholar

[2] H. J. Choe and J. L. Lewis, On the singular set in the Navier–Stokes equations, J. Funct. Anal. 175 (2000), no. 2, 348–369. 10.1006/jfan.2000.3582Suche in Google Scholar

[3] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud. 105, Princeton University Press, Princeton, 1983. 10.1515/9781400881628Suche in Google Scholar

[4] E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, River Edge, 2003. 10.1142/9789812795557Suche in Google Scholar

[5] C. Guevara and N. C. Phuc, Local energy bounds and ϵ-regularity criteria for the 3D Navier–Stokes system, Calc. Var. Partial Differential Equations 56 (2017), no. 3, Paper No. 68. 10.1007/s00526-017-1151-7Suche in Google Scholar

[6] R. Hynd, Partial regularity of weak solutions of the viscoelastic Navier–Stokes equations with damping, SIAM J. Math. Anal. 45 (2013), no. 2, 495–517. 10.1137/120875041Suche in Google Scholar

[7] O. A. Ladyzhenskaya and G. A. Seregin, On partial regularity of suitable weak solutions to the three-dimensional Navier–Stokes equations, J. Math. Fluid Mech. 1 (1999), no. 4, 356–387. 10.1007/s000210050015Suche in Google Scholar

[8] F. Lin, A new proof of the Caffarelli–Kohn–Nirenberg theorem, Comm. Pure Appl. Math. 51 (1998), no. 3, 241–257. 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO;2-ASuche in Google Scholar

[9] F. Lin and P. Zhang, On the initial-boundary value problem of the incompressible viscoelastic fluid system, Comm. Pure Appl. Math. 61 (2008), no. 4, 539–558. 10.1002/cpa.20219Suche in Google Scholar

[10] F.-H. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids, Comm. Pure Appl. Math. 58 (2005), no. 11, 1437–1471. 10.1002/cpa.20074Suche in Google Scholar

[11] W. S. Ożański, Partial regularity of Leray-Hopf weak solutions to the incompressible Navier–Stokes equations with hyperdissipation, Anal. PDE 16 (2023), no. 3, 747–783. 10.2140/apde.2023.16.747Suche in Google Scholar

[12] N. C. Phuc and M. Torres, Characterizations of signed measures in the dual of BV and related isometric isomorphisms, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), no. 1, 385–417. 10.2422/2036-2145.201508_005Suche in Google Scholar

[13] V. Scheffer, Partial regularity of solutions to the Navier–Stokes equations, Pacific J. Math. 66 (1976), no. 2, 535–552. 10.2140/pjm.1976.66.535Suche in Google Scholar

[14] V. Scheffer, Hausdorff measure and the Navier–Stokes equations, Comm. Math. Phys. 55 (1977), no. 2, 97–112. 10.1007/BF01626512Suche in Google Scholar

[15] V. Scheffer, The Navier–Stokes equations in space dimension four, Comm. Math. Phys. 61 (1978), no. 1, 41–68. 10.1007/BF01609467Suche in Google Scholar

[16] V. Scheffer, The Navier–Stokes equations on a bounded domain, Comm. Math. Phys. 73 (1980), no. 1, 1–42. 10.1007/BF01942692Suche in Google Scholar

[17] J. Serrin, On the interior regularity of weak solutions of the Navier–Stokes equations, Arch. Ration. Mech. Anal. 9 (1962), 187–195. 10.1007/BF00253344Suche in Google Scholar

[18] W. Wang and Z. Zhang, On the interior regularity criteria and the number of singular points to the Navier–Stokes equations, J. Anal. Math. 123 (2014), 139–170. 10.1007/s11854-014-0016-7Suche in Google Scholar