Spherically symmetric threedimensional non-stationary flow of a micropolar compressible viscous fluid

Predmet istraživanja disertacije je sferno simetrični trodimenzionalni model kompresibilnog viskoznog izotropnog i toplinski provodljivog mikropolarnog fluida koji je u termodinamičkom smislu savršen i politropan. U prvom dijelu temeljem konstitutivnih jednadžbi za opisani fluid te zakona očuvanja izvodi se u Eulerovoj deskripciji matematički model toka promatranog fluida između dvije termički izolirane koncentrične čvrste sferne stijenke u trodimenzionalnom euklidskom prostoru, a zatim se uz pretpostavku sferne simetrije rješenja formira inicijalno-rubni problem sa dvije varijable u Lagrangeovoj deskripciji, s homogenim rubnim uvjetima za brzinu, mikrorotaciju i toplinski fluks te dovoljno glatkim početnim funkcijama. U drugom dijelu rada korištenjem Faedo-Galerkinove metode dokazuje se egzistencija generaliziranog rješenja opisanog inicijalno-rubnog problema lokalno po vremenu. U sljedecem dijelu rada pokazuje se jedinstvenost generaliziranog rješenja, dok se u završnom dijelu rada dokazuje i egzistencija rješenja za svaki konačni vremenski interval.The subject of the thesis is spherically symmetric three dimensional model of the compressible viscous isotropic and heat-conducting micropolar fluid that is in thermodynamical sense perfect and polytropic. In the first part of the thesis based on constitutive equations for described fluid as well as the balance laws we derive mathematical model of the fluid flow in Eulerian description for the flow between two concentric spherical thermoinsulated solid walls in three dimensional Euclidean space. Using the assumptions of spherical symmetry we derive initial-boundary problem with two variables in Lagrangian description with homogeneous boundary conditions for velocity, microrotation and heat flux for sufficiently smooth initial functions. In the second part of the work using the Faedo-Galerkin method we prove the existence of the generalized solution of described initial-boundary problem locally in time. In the next part of the work we prove the uniqueness of the generalized solution, and in the final part there is the proof of the existence of the solution for each finite time