Stable water based High-Temperature-High-Pressure (HTHP) and/or Non-HTHP crosslinked copolymers for oil and gas applications consist of (i) a crosslinked, linear polyvinyl amide/polymerizable carboxylic acid) copolymer, having a composition, by weight, of 25-75 wt. % of a vinyl amide monomer selected from vinyl pyrrolidone, vinyl caprolactam, N-vinyl-N-methylacetamide and mixtures thereof, and 25-75 wt. % of a polymerizable carboxylic acid monomer selected from acrylic acid, (meth)acrylic acid, crotonic acid, itaconic acid, maleic acid and mixture thereof; and (ii) a crosslinker in an amount of 0.01-5% based on weight of total monomers. Also discloses relevant compositions comprising said copolymer and method of use thereof.