On the initial-boundary value problem for a vortex filament in an external flow under the localized induction approximation

References

• Aref , H. and Flinchem , E. P. 1984 . Dynamics of a vortex filament in a shear flow . J. Fluid Mech. , 148 : 477 – 497 .
   Web of Science ®Google Scholar
• Arms , R. J. and Hama , F. R. 1965 . Localized-induction concept on a curved vortex and motion of an elliptic vortex ring . Phys. Fluids , 8 : 553 – 559 .
   Web of Science ®Google Scholar
• Da Rios , L. S. 1906 . Sul moto d'un liquido indefinito con un filetto vorticoso di forma qualunque. Rend . Circ. Mat. Palermo , 22 : 117 – 135 .
   Google Scholar
• Hasimoto , H. 1972 . A soliton on a vortex filament . J. Fluid Mech. , 51 : 477 – 485 .
   Web of Science ®Google Scholar
• Koiso , N. 1997 . The vortex filament equation and a semilinear Schrödinger equation in a hermitian symmetric space . Osaka J. Math. , 34 : 199 – 214 .
   Web of Science ®Google Scholar
• Koiso , N. 1997 . Vortex filament equation and semilinear Schrödinger equation. In: Nonlinear Waves (Gakuto International Series; Mathematical Sciences and Applications 10) , Edited by: Agemi , R. 231 – 236 . Tokyo : Gakkotosho .
   Google Scholar
• Lakshmanan , M. , Ruijgrok , T. W. and Thompson , C. J. 1976 . On the dynamics of a continuum spin system . Physica A , 84 : 577 – 590 .
   Web of Science ®Google Scholar
• Levi-Civita , T. 1908 . Sull'attrazione esercitata da una linea materiale in punti prossimi alia linea stessa . Rend. R. Acc. Lincei , 17 : 3 – 15 .
   Google Scholar
• Nishiyama , T. 1996 . “ Solvability of the vortex filament equations ” . Keio University . Ph.D thesis
   Google Scholar
• Nishiyama , T. On the motion of a vortex filament in an external flow according to the localized induction approximation . Proc. Roy. Soc. Edinburgh A , to appear
   Google Scholar
• Nishiyama , T. Existence of a solution to the mixed problem for the vortex filament equation with an external flow term . preprint
   Google Scholar
• Nishiyama , T. and Tani , A. 1994 . Solvability of the localized induction equation for vortex motion . Comm. Math. Phys. , 162 : 433 – 445 .
   Web of Science ®Google Scholar
• Nishiyama , T. and Tani , A. 1996 . Initial and initial-boundary value problems for a vortex filament with or without axial flow . SIAM J. Math. Anal. , 27 : 1015 – 1023 .
   Web of Science ®Google Scholar
• Onuki , A. 1985 . Line motion in terms of nonlinear Schrödinger equations . Progr. Theoret. Phys. , 74 : 979 – 996 .
   Google Scholar
• Ricca , R. L. 1991 . Rediscovery of Da Rios equations. Nature , 352 : 561 – 562 .
   Google Scholar
• Ricca , R. L. 1996 . The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics . Fluid Dyn. Res. , 18 : 245 – 268 .
   Web of Science ®Google Scholar
• Schwarz , K. W. 1985 . Three-dimensional vortex dynamics in superfluid 4He: line-line and line-boundary interactions . Phys. Rev. B , 31 : 5782 – 5804 .
   Web of Science ®Google Scholar
• Slobodetskĭ , L. N. 1958 . Estimates of solutions of elliptic and parabolic systems . Dokl. Akad. Nauk SSSR , 120 : 468 – 471 . in Russian
   Google Scholar
• Sulem , P. L. , Sulem , C. and Bardos , C. 1986 . On the continuous limit for a system of classical spins . Comm. Math. Phys. , 107 : 431 – 454 .
   Web of Science ®Google Scholar
• Tani , A. and Nishiyama , T. 1997 . Solvability of equations for motion of a vortex filament with or without axial flow. , Vol. 33 , 509 – 526 . Publ. Res. Inst. Math. Sci. Kyoto Univ .
   Google Scholar