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This course is a continuation of the course DIR010. It concerns the recent results in the theory of evolutionary Navier--Stokes equations, with a special attention to the regularity of the solution in three space dimensions. The basic notion will be the suitable weak solution, i.e. a solution satisfying local energy inequality. Next, the course covers also the heat conducting incompressible newtonian fluid with temperature dependent material coefficients.
Last update: T_MUUK (14.05.2013)
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To present the recent results in the theory of evolutionary Navier--Stokes equations. Last update: T_MUUK (14.05.2013)
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The oral exam is based on the material explained during the course. Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (11.06.2019)
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Caffarelli, L.; Kohn, R.; Nirenberg, L. Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982), no. 6, 771-831
Seregin, G.; Šverák, V.: Navier-Stokes equations with lower bounds on the pressure. Arch. Ration. Mech. Anal. 163 (2002), no. 1, 65-86
Escauriaza, L.; Serëgin, G. A.; Šverák, V.: L^ {3,\infty}-solutions of Navier-Stokes equations and backward uniqueness. Uspekhi Mat. Nauk 58 (2003), no. 2(350), 3-44
Feireisl, Eduard; Málek, Josef: On the Navier-Stokes equations with temperature-dependent transport coefficients. Differ. Equ. Nonlinear Mech. 2006, Art. ID 90616, 14 stran (elektronicky). Last update: T_MUUK (14.05.2013)
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Lecture Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (25.04.2023)
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This course is a continuation of the course DIR010. It concerns the recent results in the theory of evolutionary Navier--Stokes equations, with a special attention to the regularity of the solution in three space dimensions. The basic notion will be the suitable weak solution, i.e. a solution satisfying local energy inequality. Next, the course covers also the heat conducting incompressible newtonian fluid with temperature dependent material coefficients. Last update: T_MUUK (14.05.2013)
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Weak solutions of linear and nonlinear PDEs, in particular of Navier-Stokes equations. Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (27.07.2021)
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