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Müller, Manfred ; Naumann, Joachim
On evolution inequalities of a modified Navier-Stokes type. II. (English). Aplikace matematiky, vol. 23 (1978), issue 6, pp. 397-407
MSC: 35A05, 35Q10, 35Q30, 47H15, 76D05 | MR 0508544 | Zbl 0452.35100 | DOI: 10.21136/AM.1978.103768
Keywords:
evolution inequalities of a modified Navier-Stokes type; evolution problem
Summary:
The present part of the paper continues the study of the abstract evolution inequality from the first part. Theorem 1 states the existence and uniqueness of a weak solution to the evolution inequality under consideration. The proof is based on the method of approximation of the weak solution by a sequence of strong solutions. Theorem 2 yields two regularity results for the strong solution.
Related articles:
On evolution inequalities of a modified Navier-Stokes type. I
On evolution inequalities of a modified Navier-Stokes type. III
References:
[1] Brézis H.: Problèmes unilatéraux. J. Math. Pures Appl., 51 (1972), 1-168. MR 0428137
[2] Brézis H.: Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert. Math. Studies 5, North Holland, 1973.
[3] Gröger K.: Regularitätsaussagen für Evolutionsgleichungen mit stark monotonen Operatoren. Math. Nachr. 67 (1975), 21-34. DOI 10.1002/mana.19750670104 | MR 0513163
[4] Müller M., Naumann J.: On evolution inequalities of a modified Navier-Stokes type, I. Apl. Mat. 23 (1978), 174-184. MR 0482433
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