Large time regular solutions to the MHD equations in cylindrical domains

• Autorzy: Wisam Alame , Wojciech M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in $W₂^{2,1}$ without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.

Kategorie tematyczne

• 76W05: Magnetohydrodynamics and electrohydrodynamics
• 35G20: Nonlinear higher-order equations
• 35G30: Boundary value problems for nonlinear higher-order equations
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2011
• Tom: 38
• Numer: 2
• Strony: 117-146

Daty

wydano

2011

Twórcy

autor

Wisam Alame

• Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

autor

Wojciech M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
• Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

Identyfikatory

DOI

10.4064/am38-2-1