Parabolic equations with critical nonlinearities
Copyright policy )Parabolic equations with critical nonlinearities
The authors consider abstract semilinear evolutionary problems of the form \[ u_t+Au=F(u),\quad u(0)=u_0 \] with a positive definite selfadjoint operator \(A\) in a Hilbert space \(H\) and nonlinear term \(F.\) They study three examples of critical problems in which the nonlinearity has the same order of magnitude as the linear part. The authors use specific techniques of proving global solvability that fit well the considered examples for which general abstract methods fail.
Navier-Stokes system, Abstract parabolic equations, Nonlinear parabolic equations, abstract semilinear evolutionary problems, global solutions, Navier-Stokes equations, Continuation and prolongation of solutions to PDEs, Stability in context of PDEs, Boundary value problems for nonlinear higher-order PDEs
Navier-Stokes system, Abstract parabolic equations, Nonlinear parabolic equations, abstract semilinear evolutionary problems, global solutions, Navier-Stokes equations, Continuation and prolongation of solutions to PDEs, Stability in context of PDEs, Boundary value problems for nonlinear higher-order PDEs
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