The local existence theorem for the strong solution for an initial-boundary value problem for the dynamic model of thermoviscoelasticity of Oldroit type in the planar case is established.
: Navier-Stokes equation, model of Oldroit type, thermoviscoelastic, strong solutions, fixed point
В ограниченной области с достаточно гладкой границей рассматривается начально-граничная задача.
1. Consiglieri L. Weak solution for a class of non-Newtonian fluids with energy transfer / L. Consiglieri. J. Math. Fluid, Mech. – 2000. – V.2. – P.267-293.
2. Orlov V.P. Ob odnoy zadache dinamiki termovyazkouprugosti sredy tipa oldroyta / V.P. Orlov, M.I. Parshin. Izvestiya VUZov. Matematika. – 2014. – №5. –c.68-74.
3. Temam R. Uravnenie Nav´e-Stoksa / R. Temam. – M:Mir, 1981. – 408s.
4. Agranovich Yu.Ya., Issledovanie matematicheskikh modeley vyazkouprugikh zhidkostey / Yu.Ya. Agranovich, P.E. Sobolevskiy. Dokl. AN USSR. – 1989. – ser. A, 10. – C.71-74
5. Agranovich Yu.Ya., Issledovanie slabykh resheniy modeli Oldroyda vyazkouprugoy zhidkosti / Yu.Ya. Agranovich, P.E. Sobolevskiy. Kachestvennye metody issledovaniya operatornykh uravneniy. – Yaroslavl´, 1991. – C.39-43.