Well-posedness and blowup criterion to the double-diffusive magnetoconvection system in 3D

We consider the well-posedness and blowup criterion to the double-diffusive magnetoconvection system in 3D. First, we establish the existence and uniqueness of the local strong solution to the system (1.1) in H-1 (R-3) with arbitrary initial data, and obtain the global strong solution when the L-2 norm of the initial data is small. This result can be regarded as a generalization of the methods in Chen et al. (J Math Phys 60(1):011511, 2019). Then, we provide some sufficient conditions for the break-down of local strong solution to system (1.1) in terms of velocity (or gradient of velocity) in weak L-p spaces. Finally, we focus on blowup criterion only depends on partial derivative of the planar components ((u) over tilde, (b) over tilde) without u(3) and b(3) in BMO-1 space. More precisely, if local solution satisfies integral(T)(0) parallel to del(h)(u) over tilde (t)parallel to(2)(BMO-1) + parallel to del(h)(b) over tilde (t)parallel to(2)(BMO-1) dt < infinity, then the strong solution (u, b, theta, s) can be extended smoothly beyond t = T. This improves and extends several previous BKM's criteria (Chol-Jun in Nonlinear Anal Real World Appl 59:103271, 2021; Guo et al. in J Math Anal Appl 458(1):755-766, 2018).