×

Behaviour at time t=0 of the solutions of semi-linear evolution equations. (English) Zbl 0446.35057


MSC:

35K55 Nonlinear parabolic equations
35K45 Initial value problems for second-order parabolic systems
35Q30 Navier-Stokes equations
Full Text: DOI

References:

[1] Agmon, S.; Douglas, A.; Nirenberg, L.: Estimate near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II. Comm. pure appl. Math. 17, 35-92 (1964) · Zbl 0123.28706
[2] Cattabriga, L.: Su un problema al contorno relativo al sistemo di equazioni di Stokes. Rend. sem. Mat. univ. Padova 31, 308-360 (1961) · Zbl 0116.18002
[3] Foias, C.; Guillope, C.; Temam, R.: New a priori estimates for Navier-Stokes equations in dimension 3. Comm. partial differential equations 6, 329-359 (1981)
[4] Foias, C.; Temam, R.: Remarques sur LES équations de Navier-Stokes stationnaires et LES phénomènes successifs de bifurcation. Ann. scuola norm. Sup. Pisa ser. 4 5, No. No. 1, 29-63 (1978) · Zbl 0384.35047
[5] Friedman, A.: Partial differential equations of parabolic type. (1964) · Zbl 0144.34903
[6] Heywood, J. G.: Classical solutions of the Navier-Stokes equations. Lecture notes in mathematics no. 771 (1980) · Zbl 0459.35072
[7] Ladyzhenskaya, O. A.: The mathematical theory of viscous incompressible flow. (1969) · Zbl 0184.52603
[8] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, ”Linear and Quasi Linear Equations of Parabolic Type,” Translations of Math. Monographs No. 23, Amer. Math. Soc., Providence, R.I.
[9] Lions, J. L.; Magenes, E.: Non homogeneous boundary value problems and applications. (1973) · Zbl 0251.35001
[10] Pazy, A.: Semi-group of linear operators and applications to partical differential equations. Lecture note no. 10 (1974)
[11] Rauch, J.; Massey, F.: Differentiability of solutions to hyperbolic initial value problems. Trans. amer. Math. soc. 189, 303-318 (1974) · Zbl 0282.35014
[12] Smale, S.: Smooth solutions of the heat and wave equations. Comment. math. Helv. 55, 1-12 (1980) · Zbl 0439.35017
[13] Solonnikov, V. A.: Estimations of the Green tensor for some boundary problems. Dokl. acad. Nauk SSSR 130, 988-991 (1960)
[14] Temam, R.: Navier-Stokes equations. (1979) · Zbl 0426.35003
[15] Vorovich, J. J.; Yudovich, V. I.: Stationary flows of incompressible viscous fluids. Mat. sb. 53, 393-428 (1961)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.