@article{RSMUP_1988__79__247_0, author = {Beir\~ao da Veiga, H.}, title = {Boundary-value problems for a class of first order partial differential equations in {Sobolev} spaces and applications to the {Euler} flow}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {247--273}, publisher = {Seminario Matematico of the University of Padua}, volume = {79}, year = {1988}, mrnumber = {964034}, zbl = {0709.35082}, language = {en}, url = {http://www.numdam.org/item/RSMUP_1988__79__247_0/} }
TY - JOUR AU - Beirão da Veiga, H. TI - Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow JO - Rendiconti del Seminario Matematico della Università di Padova PY - 1988 SP - 247 EP - 273 VL - 79 PB - Seminario Matematico of the University of Padua UR - http://www.numdam.org/item/RSMUP_1988__79__247_0/ LA - en ID - RSMUP_1988__79__247_0 ER -
%0 Journal Article %A Beirão da Veiga, H. %T Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow %J Rendiconti del Seminario Matematico della Università di Padova %D 1988 %P 247-273 %V 79 %I Seminario Matematico of the University of Padua %U http://www.numdam.org/item/RSMUP_1988__79__247_0/ %G en %F RSMUP_1988__79__247_0
Beirão da Veiga, H. Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow. Rendiconti del Seminario Matematico della Università di Padova, Tome 79 (1988), pp. 247-273. http://www.numdam.org/item/RSMUP_1988__79__247_0/
[1] D. BREZIS - H. BREZIS, Perturbations singulières et prolongements maximaux d'opérateurs positifs, Arch. Rat. Mech. Analysis, 53 (1973), pp. 69-100. | MR | Zbl
-[2] J. RAUCH, Maximal positive boundary value problems as limits of singular perturbation problems, Trans. Amer. Math. Soc., 270 (1982), pp. 377-408. | MR | Zbl
-[3] On an Euler type equation in Hydrodynamics, Ann. Mat. Pura Appl., 125 (1980), pp. 279-295. | MR | Zbl
,[4] Existence of C∞ solutions of the Euler equations for non-homogeneous fluids, Comm. Partial Diff. Eq., 5 (1980), pp. 95-107. | Zbl
- ,[5] Homogeneous and non-homogeneous boundary value problems for first order linear hyperbolic systems arising in fluid mechanics, Comm. in Partial Differential Equations, part I: 7 (1982), pp. 1135-1149; part II: 8 (1983), pp. 407-432. | Zbl
,[6] An Lp-theory for the n-dimensional, stationary, compressible, Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solutions, Comm. Math. Phys., 109 (1987), pp. 229-248. | MR | Zbl
,[7] On a stationary transport equation, Ann. Univ. Ferrara, 32 (1986), pp. 79-91. | MR | Zbl
,[8] Existence results in Sobolev spaces for a stationary transport equation, U.T.M. 203, June 1986, Univ. Trento, to appear in the volume dedicated by « Ricerche di Matematica », to the memory of Professor C. Miranda. | MR | Zbl
,[9] Kato's perturbation theory and well-posedness for the Euler equations in bounded domains, Arch. Rat. Mech. Anal., to appear. | Zbl
,[10] Remarks on the Euler equation, J. Funct. Analysis, 15 (1974), pp. 341-363. | MR | Zbl
- ,[11] J. E. MARSDEN, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math., 92 (1970), pp. 102-163. | MR | Zbl
-[12] Symmetric positive linear differential equations, Comm. Pure Appl. Math., 11 (1958), pp. 333-418. | MR | Zbl
,[13] An Lr-theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo, 24 (1977), pp. 685-700. | MR | Zbl
- ,[14] Linear evolution equations of « hyperbolic » type, J. Fac. Sci. Univ. Tokyo, 17 (1970), pp. 241-258. | MR | Zbl
,[15] Linear evolution equations of « hyperbolic » type II, J. Math. Soc. Japan, 25 (1973), pp. 648-666. | MR | Zbl
,[16] Quasi-linear equations of evolution, with applications to partial differential equations, in « Spectral theory and differential equations », Lecture Notes in Mathematics, vol. 448, Springer-Verlag (1975). | MR | Zbl
,[17] C. Y. LAI, Nonlinear evolution equations and the Euler flow, J. Funct. Analysis, 56 (1984), pp. 15-28. | MR | Zbl
-[18] A variational method for parameter identification, to appear. | Numdam | MR | Zbl
- ,[19] Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math., 13 (1960), pp. 427-455. | MR | Zbl
- ,[20] Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math., 28 (1975), pp. 607-675. | MR | Zbl
- ,[21] Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer. Math. Soc., 291 (1985), pp. 167-187. | MR | Zbl
,[22] Differentiability of solutions to hyperbolic initial-boundary value problems, Trans. Amer. Math. Soc., 189 (1974), pp. 303-318. | MR | Zbl
- ,[23] Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation, to appear. | MR | Zbl
,[24] On the Euler equations of incompressible perfect fluids, J. Funct. Analysis, 20 (1975), pp. 32-43. | Zbl
,[25] An well-posedness theorem for nonhomogeneous inviscid fluids via a perturbation theorem, to appear. | Zbl
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