## Operator Approach to Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal FluidThe main topics presented in this book deal with methods from functional analysis applied to the study ofsmall movements and normal oscillations ofhydrome chanical systems having cavities filled with either ideal or viscous fluids. The book is a sequel to and at the same time substantially extends the volume entitled "Opera tor Methods in Linear Hydrodynamics: Evolution and Spectral Problems," by N. D. Kopachevsky, S.G. Krein, and Ngo Zuy Kan that was published in 1989 by the Nauka publishing house in Moscow. The present book includesseveral new problems on the oscillations ofpartially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The contents of this book do not overlap almost at all with the ones in the following volumes: "Mathematical Problems of the Motion of Viscous Incopressible Fluids," by O. A. Ladyzhenskaya, "The Dynamics ofBodies with Cavities Filled with Fluids," by N. N. Moiseev and V. V. Rumiantzev, "Navier-Stokes Equations," by R. Temam, and "Boundary Problems for Navier-Stokes Equations," by S. M. Belonosov and K. A. Chernous. Mainly, the contents of the present book rely on the authors' and their students' works. We would like to express our gratitude to I. T. Gohberg and A. S. Markus, who encouraged us to publish the book and who offered many helpful suggestions. Our gratidude goes also to our colleagues T. Ya. Azizov, O. A. Ladyzhenskaya, N. N. |

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### Contents

IV | 1 |

V | 5 |

VI | 7 |

VII | 8 |

VIII | 9 |

IX | 10 |

XI | 11 |

XII | 12 |

CXXI | 158 |

CXXII | 163 |

CXXIII | 164 |

CXXV | 165 |

CXXVI | 166 |

CXXVIII | 167 |

CXXIX | 168 |

CXXX | 170 |

XIV | 14 |

XVI | 15 |

XVII | 16 |

XVIII | 17 |

XIX | 18 |

XX | 19 |

XXI | 20 |

XXII | 21 |

XXIII | 22 |

XXIV | 23 |

XXV | 24 |

XXVI | 25 |

XXVII | 26 |

XXVIII | 28 |

XXIX | 29 |

XXXI | 30 |

XXXIII | 31 |

XXXV | 32 |

XXXVI | 34 |

XXXVIII | 35 |

XL | 37 |

XLII | 38 |

XLIII | 39 |

XLV | 41 |

XLVI | 43 |

XLVIII | 44 |

XLIX | 47 |

L | 48 |

LI | 49 |

LII | 51 |

LIV | 52 |

LV | 53 |

LVI | 54 |

LVII | 55 |

LVIII | 56 |

LIX | 57 |

LX | 58 |

LXI | 62 |

LXII | 63 |

LXIV | 65 |

LXV | 66 |

LXVII | 68 |

LXVIII | 69 |

LXIX | 70 |

LXX | 71 |

LXXI | 72 |

LXXII | 73 |

LXXIII | 75 |

LXXIV | 76 |

LXXV | 77 |

LXXVI | 78 |

LXXVII | 79 |

LXXVIII | 82 |

LXXIX | 86 |

LXXX | 87 |

LXXXII | 90 |

LXXXIII | 93 |

LXXXV | 95 |

LXXXVI | 98 |

LXXXVII | 99 |

LXXXVIII | 101 |

LXXXIX | 103 |

XC | 107 |

XCI | 109 |

XCII | 110 |

XCIV | 111 |

XCV | 112 |

XCVII | 113 |

XCVIII | 114 |

XCIX | 115 |

C | 116 |

CI | 117 |

CII | 118 |

CIII | 124 |

CIV | 125 |

CV | 126 |

CVI | 127 |

CVII | 128 |

CVIII | 129 |

CIX | 131 |

CX | 132 |

CXI | 134 |

CXII | 138 |

CXIII | 143 |

CXIV | 146 |

CXV | 149 |

CXVI | 151 |

CXVII | 152 |

CXVIII | 153 |

CXIX | 154 |

CXX | 155 |

CXXXI | 171 |

CXXXIII | 172 |

CXXXIV | 173 |

CXXXV | 174 |

CXXXVII | 175 |

CXXXVIII | 176 |

CXXXIX | 177 |

CXL | 178 |

CXLI | 179 |

CXLII | 184 |

CXLIII | 187 |

CXLIV | 189 |

CXLV | 190 |

CXLVI | 191 |

CXLVII | 193 |

CXLVIII | 194 |

CXLIX | 196 |

CL | 199 |

CLI | 200 |

CLII | 201 |

CLIII | 203 |

CLIV | 204 |

CLV | 205 |

CLVI | 206 |

CLVII | 208 |

CLIX | 209 |

CLX | 213 |

CLXII | 216 |

CLXIII | 217 |

CLXIV | 219 |

CLXV | 220 |

CLXVI | 221 |

CLXVII | 223 |

CLXVIII | 224 |

CLXIX | 226 |

CLXX | 232 |

CLXXII | 234 |

CLXXIV | 237 |

CLXXV | 241 |

CLXXVI | 244 |

CLXXVII | 246 |

CLXXVIII | 249 |

CLXXIX | 252 |

CLXXX | 256 |

CLXXXI | 257 |

CLXXXIII | 259 |

CLXXXIV | 261 |

CLXXXV | 263 |

CLXXXVI | 264 |

CLXXXVII | 265 |

CLXXXVIII | 270 |

CXC | 272 |

CXCI | 274 |

CXCII | 276 |

CXCIII | 278 |

CXCIV | 281 |

CXCV | 282 |

CXCVI | 284 |

CXCVII | 287 |

CXCVIII | 288 |

CXCIX | 289 |

CCI | 290 |

CCIII | 292 |

CCIV | 294 |

CCV | 297 |

CCVI | 299 |

CCVII | 302 |

CCVIII | 310 |

CCX | 313 |

CCXII | 316 |

CCXIII | 318 |

CCXIV | 321 |

CCXV | 322 |

CCXVI | 323 |

CCXVII | 325 |

CCXVIII | 327 |

CCXIX | 328 |

CCXX | 331 |

CCXXI | 333 |

CCXXIII | 335 |

CCXXIV | 338 |

CCXXV | 341 |

CCXXVI | 345 |

CCXXVII | 347 |

CCXXVIII | 350 |

355 | |

357 | |

CCXXXII | 375 |

379 | |

### Other editions - View all

Operator Approach to Linear Problems of Hydrodynamics: Volume 1: Self ... Nikolay D. Kopachevskii,Selim G. Krein No preview available - 2012 |

Operator approach to linear problems of hydrodynamics Nikolaj D. Kopačevskij,Selim G. Krejn No preview available - 2001 |

### Common terms and phrases

angular velocity arbitrary associated elements boundary conditions boundary value problem bounded linear bounded linear operator bounded operator called capillary fluid Cauchy problem cavity coefficients compact operator component constant container continuous function coordinate system corresponding decomposition defined denote dense differential discrete spectrum dynamic eigenelements eigenvalues elastic equals zero equilibrium finite function free surface Green formula heavy fluid Hence Hilbert space Hl(fl holds true holomorphic ideal fluid incompressible inequality interval introduce inverse operator Jo(fi kinetic energy Laplace operator Let us assume Let us consider Let us note linear operator motion N. D. Kopachevsky nonnegative nonperturbed norm obtain operator acting operator pencil operator-valued function partially filled positive definite pressure problem on oscillations proper oscillations properties region Riesz rotation satisfies scalar product Section self-adjoint operator semigroup small oscillations solid boundary space H spectral problem Subsection surface F theorem variational ratio vector velocity field

### Popular passages

Page 371 - Rabinovich, BI: On the equations of perturbed motion of a rigid body with a cylindrical hollow partly filled with fluid.

Page 369 - Furthermore, the motion of a rigid body with a cavity partially filled with a viscous capillary liquid is investigated and the spectrum of normal oscillations is studied.