Boundary value problems for non-Cauchy-Kovalevskaya-type systems in a quarter-space
An initial-boundary value problem in a quarter space for a sufficiently large class of integro-differential systems with degenerate matrix coefficients at the time derivative is discussed. Examples of such systems are the linearized Navier-Stokes system, the system of Rossby waves, the Sobolev system and the system of internal waves. Since the matrix of coefficients is degenerated, the system of equations fail to be of Cauchy-Kovalevskaya type, therefore the boundary value problems have peculiarities. For the Sobolev system, the system of internal waves and the system of gravitational gyroscopical waves for Boussinesq approximation, solvability and well-posedness in weighted Sobolev space, if the Lopatinskii condition holds, is shown.
well-posedness in weighted Sobolev space
scientific article; zbMATH DE number 918053